Finite Group DatabasebetaFinite Group Databasebeta| order | 26508 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D2209 |
| unambiguous semidirect product | (D3×C2209)⋊C2 |
| unambiguous semidirect product | (C3×D2209)⋊C2 |
| unambiguous semidirect product | D6627⋊C2 |
| Fitting, derived, Hall | C3×C2209 ⋊ C22 |
| Sylow | C2209 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D2209 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C2209 | C22 |
| Frattini | C47 | D3×D47 |
| socle | C3×C47 | C2×D47 |
| LCS | G ▷ C3×C2209 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6627 |
3318 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26508, 6);