C₂²×D₅² #87924

order	400
isoclinism	isoclinic class of D₅²
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product	C₂²×D₅²
unambiguous semidirect product	(C₅×D₅)⋊C₂³
unambiguous semidirect product	(C₅⋊D₅)⋊C₂³

Fitting, socle	C₂²×C₅² ⋊ C₂²
derived, Sylow	C₅² ⋊ C₂⁴

	subgroup	G/H
center, hypercenter	C₂²	D₅²
commutator, cosocle, hypocenter	C₅²	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂²×C₅²	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²

300 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 4 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 218);