C₃×#11717194 #72229677

order	2400
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²×C₄×C₅

Aliases

864 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 21 points:

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

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

maximal subgroup of	C₃×#127×C₅⋊D₅, D₃×#11717194, #72231134
maximal normal subgroup of	C₃×#127×C₅⋊D₅, D₃×#11717194, #72231134

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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