C₁₃⋊C₃×#5935 #72259242

order	7488
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₃⋊C₃×#1020
commutator, cosocle, hypocenter	C₁₃×#997	C₂×C₃
Fitting	C₁₃×H(5,𝔽₂)	C₃×D₃
socle	C₂×C₁₃	C₃×#1020
LCS	G ▷ C₁₃×#997
UCS	C₁ ◁ C₂

334 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 2 generators on 21 points:

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

maximal subgroup of	D₁₃⋊C₃×#5935
maximal normal subgroup of	D₁₃⋊C₃×#5935

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

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