C₅×C₇⋊C₃₂ #11764396

order	1120
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₅×C₃₂ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₇⋊C₃₂
unambiguous semidirect product	C₇⋊(C₅×C₃₂)

derived, Sylow	C₇ ⋊ C₅×C₃₂
Hall	C₅×C₇ ⋊ C₃₂

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 1120

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3,4,5)(7,8)(9,10)(11,12)(13,14,15,19,16,20,23,29,17,21,24,30,26,32,35,39,18,22,25,31,27,33,36,40,28,34,37,41,38,42,43,44);(6,7,9,11,12,10,8)

400 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 2);