C₂×D₅²⋊C₂ #87917

order	400
isoclinism	isoclinic class of D₅²⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×D₅²⋊C₂
unambiguous semidirect product	D₅²⋊C₂²

Fitting, socle	C₂×C₅² ⋊ D₄
Sylow	C₅² ⋊ C₂×D₄

94 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 20

A minimal faithful permutation representation — 3 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 211);