C₃×#428 #5302

order	192
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	Aut(G) = C₂²×D₄×#120 (order 1024) · Inn(G) = C₂×D₄ · Out(G) = C₂³×D₄
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

118 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)(6,9)(7,11)(10,12)(13,14,15);(5,6,7,9,8,10,11,12);(6,10)(9,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 861);