C₁₁×Dic₆ #63150

order	264
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×C₅×D₃×D₄ (order 480) · Inn(G) = C₂×D₃ · Out(G) = C₂³×C₅
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×Dic₆
unambiguous semidirect product	C₃⋊(Q₈×C₁₁)

Hall	C₃×C₁₁ ⋊ Q₈
Sylow	C₃ ⋊ Q₈×C₁₁

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 264

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(264, 18);