C₂²×Dic₆ #998

order	96
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = D₃×#72209832 (order 18432) · Inn(G) = C₂×D₃ · Out(G) = #72209653
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂²×Dic₆

C₃ ⋊ C₂²×Q₈

156 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 4 generators on 15 points:

(5,6,7)(8,10,11,15)(9,12,13,14);(1,2)(3,4)(6,7)(8,9,11,13)(10,14,15,12);(3,4);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 205);