Dic₅×C₃⋊C₈ #90949

order	480
isoclinism	isoclinic class of D₃×D₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₄

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₃×D₅
commutator, hypocenter	C₃×C₅	C₄×C₈
Fitting, cosocle	C₂×C₃×C₄×C₅	C₂²
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 25);