C₂²×#1044 #87923

order	400
isoclinism	isoclinic class of #1044
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³×C₅

Aliases

Fitting, socle	C₂²×C₅² ⋊ C₄
derived, Sylow	C₅² ⋊ C₂²×C₄

140 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 217);