C₁₁×#3722 #13097067

order	1584
isoclinism	isoclinic class of #625
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃²×C₁₁ ⋊ C₂²⋊C₄
Sylow	C₃² ⋊ C₁₁×C₂²⋊C₄

168 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 264

A minimal faithful permutation representation — 2 generators on 25 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 231);