C₃×C₅×#137 #91866

order	480
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₅ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle	C₂×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃×C₅
prime radical	C₃×C₅×#41	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂×C₃×C₄×C₅ ◁ G

120 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 240

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 942);