C₃²×Dic₁₁ #87679

order	396
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×Dic₁₁
unambiguous semidirect product	C₁₁⋊(C₃²×C₄)

derived, Sylow	C₁₁ ⋊ C₃²×C₄
Hall	C₃²×C₁₁ ⋊ C₄

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 396

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(396, 11);