C₇×#19885 #13197101

order	1792
nilpotency class	3
isoclinism	isoclinic class of #19883
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center, socle	C₂²×C₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄²×C₇ ◁ G

830 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 448

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 12873);