C₅×#11715850 #72246129

order	3840
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

Fitting	C₂²×C₅×H(5,𝔽₂) ⋊ D₃
derived	C₂²⋊#997 ⋊ C₂×C₅

	subgroup	G/H
center, hypercenter	C₂×C₅	#87588
commutator, cosocle, hypocenter	C₂²⋊#997	C₂×C₅
Frattini	C₂	C₅×#87588
Fitting	C₂²×C₅×H(5,𝔽₂)	D₃
socle	C₂³×C₅	#1020
LCS	G ▷ C₂²⋊#997
UCS	C₁ ◁ C₂×C₅

2378 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 2378 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 3 generators on 17 points:

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

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

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