C₇×#16551 #13193767

order	1792
nilpotency class	2
isoclinism	isoclinic class of #16249
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₇
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

2470 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 896

A minimal faithful permutation representation — 4 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 9539);