order	480
isoclinism	isoclinic class of (C₂⁴⋊C₅)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Fitting, socle	C₂⁴×C₃ ⋊ D₅
derived	C₂⁴⋊C₅ ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₃	(C₂⁴⋊C₅)⋊C₂
commutator, cosocle, hypocenter	C₂⁴⋊C₅	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃	D₅
LCS	G ▷ C₂⁴⋊C₅
UCS	C₁ ◁ C₃

86 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1194);