C₂₅×C₄⋊Dic₃ #11924848

order	1200
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₅×C₄⋊Dic₃
unambiguous semidirect product	C₄⋊(Dic₃×C₂₅)

Hall	C₃×C₂₅ ⋊ C₄⋊C₄
Sylow	C₃ ⋊ C₄⋊C₄×C₂₅

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1200

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

450 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 58);