A₄×PSL(2,𝔽₁₃) #72228186

order	13104
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₂² ⋊ C₃×PSL(2,𝔽₁₃)
socle, derived	C₂²×PSL(2,𝔽₁₃) ⋊ C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₂²×PSL(2,𝔽₁₃)	C₃
Fitting, cosocle	C₂²	C₃×PSL(2,𝔽₁₃)
LCS	G ▷ C₂²×PSL(2,𝔽₁₃)
UCS	C₁

124 conjugacy classes of subgroups; only the 6 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 6 normal subgroups are shown.

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

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 56

A minimal faithful permutation representation — 2 generators on 18 points:

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

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

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