C₂⁵×D₁₃⋊C₃ #72276164

order	2496
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₃ · Schur multiplier (H₂) = C₂¹⁵

Aliases

C₂⁵×D₁₃⋊C₃

	subgroup	G/H
center, hypercenter	C₂⁵	D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂⁶×C₃
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₃	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁵

11300 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 6 generators on 23 points:

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

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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