order	480
isoclinism	isoclinic class of D₃×C₂⁴⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product	D₃×C₂⁴⋊C₅
unambiguous semidirect product	C₃⋊(C₂×C₂⁴⋊C₅)
unambiguous semidirect product	(C₂⁴×D₃)⋊C₅

Splittings

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂⁴×C₃	C₂×C₅
LCS	G ▷ C₂⁴×C₃
UCS	C₁

164 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 30

A minimal faithful permutation representation — 2 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1196);