C₇×#24792 #13202008

order	1792
nilpotency class	3
isoclinism	isoclinic class of #24274
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

1076 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)(8,9,10,11)(16,17,21,18)(19,20,23,22);(12,13)(14,15)(16,18,20,23,21,17,22,19);(9,11)(13,15)(17,18)(19,23);(16,19,20,18,21,23,22,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 17780);