order	192
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂³×D₃×#120 (order 1536) · Inn(G) = C₂×D₃ · Out(G) = C₂⁴×D₄
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₈×D₁₂

Splittings

Fitting	C₃×C₄×C₈ ⋊ C₂
Sylow	C₃ ⋊ C₈×D₄

134 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 245);