C₂³×C₅⋊D₅ #87926

order	400
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶×C₅

Aliases

C₂³×C₅⋊D₅

Fitting, socle	C₂³×C₅² ⋊ C₂
derived, Sylow	C₅² ⋊ C₂⁴

	subgroup	G/H
center, hypercenter	C₂³	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂³×C₅²	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂³

536 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 200

A minimal faithful permutation representation — 4 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 220);