C₃×C₅×#477 #11751452

order	960
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

192 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.

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

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3)(4,5,6,7,8)(9,10,12,14)(11,15,16,13)(18,21)(19,22)(23,24);(9,11,12,16)(10,13,14,15)(17,18,20,21)(19,22,23,24);(17,19,20,23)(18,22,21,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 5647);