Finite Group DatabasebetaFinite Group Databasebeta| order | 26724 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D393 |
| unambiguous semidirect product | (C3×D17)⋊D131 |
| unambiguous semidirect product | (D17×C131)⋊D3 |
| Fitting, socle, derived, Hall | C3×C17×C131 ⋊ C22 |
| Hall | C17×C131 ⋊ C2×D3 |
| Hall | C3×C131 ⋊ C2×D17 |
| Sylow | C131 ⋊ D3×D17 |
| Hall | C3×C17 ⋊ C2×D131 |
| Sylow | C17 ⋊ C2×D393 |
| Sylow | C3 ⋊ D17×D131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C131 | C22 |
| LCS | G ▷ C3×C17×C131 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6681 |
1980 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26724, 18);