Finite Group DatabasebetaFinite Group Databasebeta| order | 28028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D539 |
| unambiguous semidirect product | (C11×D13)⋊D49 |
| unambiguous semidirect product | (D13×C49)⋊D11 |
| Fitting, derived, Hall | C11×C13×C49 ⋊ C22 |
| Hall | C13×C49 ⋊ C2×D11 |
| Hall | C11×C49 ⋊ C2×D13 |
| Hall | C11×C13 ⋊ C2×D49 |
| Sylow | C49 ⋊ D11×D13 |
| Sylow | C13 ⋊ C2×D539 |
| Sylow | C11 ⋊ D13×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×C13×C49 | C22 |
| Frattini | C7 | D13×D77 |
| socle | C7×C11×C13 | C2×D7 |
| LCS | G ▷ C11×C13×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7007 |
2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28028, 16);