C₅²×Dic₁₂ #11925211

order	1200
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅² · Schur multiplier (H₂) = C₅

Aliases

C₅²×Dic₁₂

Hall	C₃×C₅² ⋊ Q₁₆
Sylow	C₃ ⋊ C₅²×Q₁₆

144 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1200

A minimal faithful permutation representation — 2 generators on 29 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 421);