C₂²×C₇×#449 #13237567

order	1792
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₇ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂²×C₇×#449

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ C₂⁴×C₄×C₇ ◁ G

5454 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 53339);