C₃×#87779 #11925071

order	1200
isoclinism	isoclinic class of #6037
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₅² ⋊ C₂²⋊C₄
Sylow	C₅² ⋊ C₃×C₂²⋊C₄

200 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 120

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

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

maximal subgroup of	C₃×#11717092
maximal normal subgroup of	C₃×#11717092

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 281);