C₃²×(C₂⁴⋊C₅)⋊C₂ #13089587

order	1440
isoclinism	isoclinic class of (C₂⁴⋊C₅)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂²×C₃

Aliases

Fitting, socle	C₂⁴×C₃² ⋊ D₅
derived	C₂⁴⋊C₅ ⋊ C₂×C₃²

	subgroup	G/H
center, hypercenter	C₃²	(C₂⁴⋊C₅)⋊C₂
commutator, cosocle, hypocenter	C₂⁴⋊C₅	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃²	D₅
LCS	G ▷ C₂⁴⋊C₅
UCS	C₁ ◁ C₃²

258 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 90

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5904);