Finite Group DatabasebetaFinite Group Databasebeta| order | 26202 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D397⋊C11) |
| unambiguous semidirect product | D1191⋊C11 |
| unambiguous semidirect product | (C397⋊C11)⋊D3 |
| Fitting, socle, derived, Hall | C3×C397 ⋊ C2×C11 |
| Hall | C3×C397⋊C11 ⋊ C2 |
| Hall | C397⋊C11 ⋊ D3 |
| Hall | D1191 ⋊ C11 |
| Sylow | C397 ⋊ D3×C11 |
| Sylow | C3 ⋊ D397⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C397 | C2×C11 |
| LCS | G ▷ C3×C397 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1191 |
Polycyclic presentation:
2,3,11,397|b^a=b^2,d^a=d^396,d^c=d^29087 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26202, 14);