A₅×D₁₃⋊C₃ #72228192

order	4680
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

Fitting, Sylow	C₁₃ ⋊ C₂×C₃×A₅
socle, derived	C₁₃×A₅ ⋊ C₂×C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₁₃×A₅	C₂×C₃
Fitting, cosocle	C₁₃	C₂×C₃×A₅
LCS	G ▷ C₁₃×A₅
UCS	C₁

100 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 65

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

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

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

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