C₄²×C₃⋊(C₅⋊D₅) #72229645

order	2400
isoclinism	isoclinic class of C₃⋊(C₅⋊D₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · 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);(2,3)(5,6)(7,8)(10,11)(12,13);(4,5,7,8,6)(14,15,16,17)

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

maximal subgroup of	C₄²×D₃×C₅⋊D₅, #127×C₃⋊(C₅⋊D₅), #72231134, …
maximal normal subgroup of	C₄²×D₃×C₅⋊D₅, #127×C₃⋊(C₅⋊D₅), #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), (2,3)(5,6)(7,8)(10,11)(12,13), (4,5,7,8,6)(14,15,16,17));