C₃×C₅×AGL(1,ℤ/8) #91865

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
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂×C₃×C₄×C₅ ◁ G

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

normal subgroups only

This group has 136 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) = 16
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 941);