D₃×S₄×AGL(1,𝔽₁₃) #72242154

order	22464
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

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

2128 conjugacy classes of subgroups.

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

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

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

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

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