C₃×#342 #4589

order	192
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	Aut(G) = C₂×#511790 (order 1024) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₂³

Aliases

142 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 148);