Finite Group DatabasebetaFinite Group Databasebeta| order | 26972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D613 |
| unambiguous semidirect product | (D11×C613)⋊C2 |
| unambiguous semidirect product | (C11×D613)⋊C2 |
| unambiguous semidirect product | D6743⋊C2 |
| Fitting, socle, derived, Hall | C11×C613 ⋊ C22 |
| Sylow | C613 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D613 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C613 | C22 |
| LCS | G ▷ C11×C613 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6743 |
2156 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26972, 8);