Finite Group DatabasebetaFinite Group Databasebeta| order | 26818 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D583 |
| unambiguous semidirect product | C11⋊(C23×D53) |
| unambiguous semidirect product | C53⋊(D11×C23) |
| Fitting, socle, Hall | C11×C23×C53 ⋊ C2 |
| derived, Hall | C11×C53 ⋊ C2×C23 |
| Hall | C23×C53 ⋊ D11 |
| Hall | C11×C23 ⋊ D53 |
| Sylow | C53 ⋊ D11×C23 |
| Sylow | C11 ⋊ C23×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D583 |
| commutator, cosocle, hypocenter | C11×C53 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C11×C23×C53 | C2 |
| LCS | G ▷ C11×C53 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13409 |
6739 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26818, 7);