Finite Group DatabasebetaFinite Group Databasebeta| order | 196 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C3×D3×#10621462 (order 12096) · Inn(G) = C1 · Out(G) = C3×D3×#10621462 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C7 |
| abelian | C22×C72 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 196 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2)(5,6,7,8,9,10,11);(3,4)(12,13,14,15,16,17,18)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(196, 12);