A₄×PSL(2,𝔽₁₁) #72227502

order	7920
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₂² ⋊ C₃×PSL(2,𝔽₁₁)
socle, derived	C₂²×PSL(2,𝔽₁₁) ⋊ C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₂²×PSL(2,𝔽₁₁)	C₃
Fitting, cosocle	C₂²	C₃×PSL(2,𝔽₁₁)
LCS	G ▷ C₂²×PSL(2,𝔽₁₁)
UCS	C₁

112 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 44

A minimal faithful permutation representation — 2 generators on 15 points:

(1,4,2)(6,14,8,11,12)(7,10,13,15,9);(1,3,4)(5,8,6,15,10,12)(7,11,13)(9,14)

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

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