C₂₅×C₂²⋊A₄ #11924995

order	1200
isoclinism	isoclinic class of C₂²⋊A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₂₅ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	C₂₅×C₂²⋊A₄
unambiguous semidirect product	C₂²⋊(A₄×C₂₅)
unambiguous semidirect product	(C₂²×C₂₅)⋊A₄

Fitting, Hall	C₂⁴×C₂₅ ⋊ C₃
derived, Sylow	C₂⁴ ⋊ C₃×C₂₅

102 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 300

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)(27,28,29)(31,32,33);(30,33)(31,32);(26,29)(27,28)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 205);