order	96
isoclinism	isoclinic class of #204
automorphism	Aut(G) = D₃×#23882 (order 1536) · Inn(G) = D₁₂ · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₂₄

Splittings

Fitting	C₂×C₃×C₈ ⋊ C₂
Sylow	C₃ ⋊ C₂×D₈

76 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)(6,7,11,13,9,12,8,10);(1,2)(4,5)(7,10)(8,11)(12,13);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 110);