C₄×#216 #5029

order	192
isoclinism	isoclinic class of #213
automorphism	Aut(G) = C₂⁵×D₃×D₄ (order 1536) · Inn(G) = #67 · Out(G) = C₂⁶
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₃ ⋊ C₄×Q₁₆

110 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 3 generators on 23 points:

(1,2,3)(8,10,12,18)(9,13,15,22)(11,20,21,17)(14,23,19,16);(2,3)(8,9,12,15)(10,16,18,23)(11,19,21,14)(13,20,22,17);(4,5,6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 588);