C₃³×Dic₁₁ #11924697

order	1188
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₃³×C₄ · Schur multiplier (H₂) = C₃³

Aliases

direct product	C₃³×Dic₁₁
unambiguous semidirect product	C₁₁⋊(C₃³×C₄)

derived, Sylow	C₁₁ ⋊ C₃³×C₄
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 — 3 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1188, 67);