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14, which we now obtain without classes: valent as well. g. 12 of the character tables of G as well as are known. of Q~HF. (XF*| integral, F* ~ F': ~ XF"(~) "" ~ II ~rJ ~(g~k(f~))), x i,j,k aik(f;~)>O so that furthermore only an implementation process Gretschel is needed. have done this, extending so that now the character mn < 15. If FG denotes of H, I and Hilge the results (Gretschel/Hilge of S~nger tables of Sm~S n a representation of G introduced in part I of the inducing and (S~nger [1]) [I]) are known for FH the following a representation abbreviation 32 n (FG;F H) := ~ F G | F H.

12 of the character tables of G as well as are known. of Q~HF. (XF*| integral, F* ~ F': ~ XF"(~) "" ~ II ~rJ ~(g~k(f~))), x i,j,k aik(f;~)>O so that furthermore only an implementation process Gretschel is needed. have done this, extending so that now the character mn < 15. If FG denotes of H, I and Hilge the results (Gretschel/Hilge of S~nger tables of Sm~S n a representation of G introduced in part I of the inducing and (S~nger [1]) [I]) are known for FH the following a representation abbreviation 32 n (FG;F H) := ~ F G | F H.

42 S ~,[2]~[12] ~. $ 2 " r] $2",,S n . 43 sgn s s 2] f'(j) = ~[2];[I s s (f';1) = ~[2]~[12](f;w)(f';1)(f;w) -I = sgn~f~(j). 44 If n S S is even and w e ~[Ss~S2] ~ S n. s := 2' the inertia group of ~[2]~[I 2] $ $2" n $2~S n in A2 ($2" N $2~S n Hence we obtain )~[Ss~S2]' $2~S n is A2 = $2~ ( ~[Ss~S2])A2 A2 S The restriction S . of ~[2]~[I 2] to S 2 0 $2~S n can be extended A2 to S2~(~[Ss~S2])A 2 as follows: 45 n S S ~[2]~[ 12] ( f ; ( g ; P ) ) := - I T sgn(f(i)). i=~+1 The check is very easy. The inertia factor is ( S 2 .

### 381st Bomber Group

by Kenneth

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