C₂×#235 #1001

order	96
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = D₃×#23900 (order 1536) · Inn(G) = C₂×D₃ · Out(G) = #2403
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₂²×C₃×C₄ ⋊ C₂
Sylow	C₃ ⋊ C₂×#41

164 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 208);