order	400
isoclinism	isoclinic class of #6045
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₅

Aliases

direct product	C₂×C₂²⋊(C₅⋊D₅)
unambiguous semidirect product	C₂³⋊(C₅⋊D₅)

Splittings

Fitting	C₂³×C₅² ⋊ C₂
Sylow	C₅² ⋊ C₂×D₄

216 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 200);