D₃×S₄×#261 #72242144

order	7488
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₃×A₄×C₁₃	C₂²×C₄
Fitting, socle	C₂²×C₃×C₁₃	C₂×C₄×D₃
prime radical	D₃×S₄×D₁₃	C₂
cosocle	C₃×A₄×D₁₃	C₂³
LCS	G ▷ C₃×A₄×C₁₃
UCS	C₁

964 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 964 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

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

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 156

A minimal faithful permutation representation — 3 generators on 20 points:

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

maximal subgroup of	D₃×S₄×AGL(1,𝔽₁₃)
maximal normal subgroup of	D₃×S₄×AGL(1,𝔽₁₃)

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

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