order	96
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = D₃×#15947 (order 1536) · Inn(G) = C₂×D₃ · Out(G) = #2403
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

Splittings

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

132 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 134);