C₃×C₅×#462 #11751437

order	960
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂²

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

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

normal subgroups only

This group has 216 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) = 28
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3)(4,5,6,7,8)(10,12)(13,14,17,20)(15,21,23,28)(16,24,26,19)(18,25,27,22);(9,10,11,12);(13,15,17,23)(14,18,20,27)(16,25,26,22)(19,28,24,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 5632);