C₃×#87756 #11924977

order	1200
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₆ · Schur multiplier (H₂) = C₅

Aliases

derived, Sylow	C₅² ⋊ C₃×C₁₆
Hall	C₃×C₅² ⋊ C₁₆

80 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 29 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 187);