C₅×#6393 #11764489

order	1120
isoclinism	isoclinic class of #1132
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₅×C₇ ⋊ #108
Sylow	C₇ ⋊ C₅×#108

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 560

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3,4,5)(6,7,9,11,12,10,8)(13,15,17,24,18,25,16,23)(14,19,20,22,21,27,26,28);(7,8)(9,10)(11,12)(13,14,16,20,18,21,17,26)(15,22,23,27,25,28,24,19)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 95);