C₅²×C₄⋊Dic₃ #11925216

order	1200
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅² · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₅²×C₄⋊Dic₃
unambiguous semidirect product	C₄⋊(C₅²×Dic₃)

Hall	C₃×C₅² ⋊ C₄⋊C₄
Sylow	C₃ ⋊ C₅²×C₄⋊C₄

208 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 1200

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2,3,4,5)(11,12,13)(18,19,20,21);(6,7,8,9,10)(12,13)(14,15,16,17)(19,21)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 426);