order	192
automorphism	Aut(G) = C₂×D₃×#10596770⋊C₂ (order 13824) · Inn(G) = C₂⁴×D₃ · Out(G) = C₂×GO⁺(4,𝔽₂)
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₃×H(5,𝔽₂) ⋊ C₂
Sylow	C₃ ⋊ C₂×H(5,𝔽₂)

898 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 5 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1524);