C₂₅×C₄²⋊C₃ #11924822

order	1200
isoclinism	isoclinic class of C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₂₅ · Schur multiplier (H₂) = C₄

Aliases

direct product	C₂₅×C₄²⋊C₃
unambiguous semidirect product	C₄²⋊(C₃×C₂₅)
unambiguous semidirect product	(C₄²×C₂₅)⋊C₃

Fitting, Hall	C₄²×C₂₅ ⋊ C₃
derived, Sylow	C₄² ⋊ C₃×C₂₅

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 300

A minimal faithful permutation representation — 2 generators on 37 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)(26,27,30)(28,32,37)(29,33,36)(31,35,34);(26,28,29,34)(27,33)(30,37,36,35)(31,32)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 32);