C₄×#217 #5209

order	192
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) order 12288
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³×C₄

Aliases

258 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)(13,15);(2,3)(8,9,10,11)(12,13)(14,15);(4,5,6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 768);