order	192
automorphism	Aut(G) = C₂²×D₃×#41 (order 384) · Inn(G) = C₂²×D₃ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

D₃×M₃₂

Splittings

Fitting	C₃×M₃₂ ⋊ C₂
Sylow	C₃ ⋊ C₂×M₃₂

90 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 19 points:

(2,6)(7,12)(8,13)(14,16)(17,18,19);(1,2,3,7,4,8,9,14,5,6,10,12,11,13,15,16);(18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 465);