C₁₁×C₃⋊(C₃⋊Dic₃) #11924702

order	1188
isoclinism	isoclinic class of C₃⋊(C₃⋊D₃)
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₃³

Aliases

direct product	C₁₁×C₃⋊(C₃⋊Dic₃)
unambiguous semidirect product	C₃⋊(C₁₁×C₃⋊Dic₃)

derived, Sylow	C₃³ ⋊ C₄×C₁₁
Hall	C₃³×C₁₁ ⋊ C₄

168 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1188

A minimal faithful permutation representation — 4 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1188, 72);