D₃×PSL(2,𝔽₁₁) #72227504

order	3960
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂

Aliases

Fitting	C₃ ⋊ C₂×PSL(2,𝔽₁₁)
socle, derived	C₃×PSL(2,𝔽₁₁) ⋊ C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₃×PSL(2,𝔽₁₁)	C₂
Fitting, cosocle	C₃	C₂×PSL(2,𝔽₁₁)
LCS	G ▷ C₃×PSL(2,𝔽₁₁)
UCS	C₁

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 33

A minimal faithful permutation representation — 2 generators on 14 points:

(1,2)(4,14,7,10,8,6)(5,9,13)(11,12);(1,2,3)(5,10,6)(8,12,11)(9,13,14)

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

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