Finite Group DatabasebetaFinite Group Databasebeta| order | 26962 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D793 |
| unambiguous semidirect product | C13⋊(C17×D61) |
| unambiguous semidirect product | C61⋊(C17×D13) |
| Fitting, socle, Hall | C13×C17×C61 ⋊ C2 |
| derived, Hall | C13×C61 ⋊ C2×C17 |
| Hall | C17×C61 ⋊ D13 |
| Hall | C13×C17 ⋊ D61 |
| Sylow | C61 ⋊ C17×D13 |
| Sylow | C13 ⋊ C17×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D793 |
| commutator, cosocle, hypocenter | C13×C61 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C61 | C2 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13481 |
6766 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26962, 6);