C₁₃×Dic₆ #64616

order	312
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₃×C₄×D₃×D₄ (order 576) · Inn(G) = C₂×D₃ · Out(G) = C₂²×C₃×C₄
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×Dic₆
unambiguous semidirect product	C₃⋊(Q₈×C₁₃)

Hall	C₃×C₁₃ ⋊ Q₈
Sylow	C₃ ⋊ Q₈×C₁₃

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 312

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 32);