C₂×#815 #5100

order	192
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×D₃×#347042 (order 6144) · Inn(G) = C₂×D₃ · Out(G) = C₂×#32898
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³

Aliases

146 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 659);