C₃×C₅×C₂²⋊Q₈ #91851

order	480
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂²

Aliases

C₃×C₅×C₂²⋊Q₈

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

148 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

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

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 927);