C₂×C₃×#106 #5299

order	192
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂×#72214572 (order 4096) · Inn(G) = D₄ · Out(G) = C₂×#10336
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂³

Aliases

130 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 858);