Finite Group DatabasebetaFinite Group Databasebeta| order | 28028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D77⋊D13 |
| unambiguous semidirect product | D77⋊(C7×D13) |
| unambiguous semidirect product | D91⋊(C7×D11) |
| unambiguous semidirect product | D143⋊(C7×D7) |
| Fitting, socle, Hall | C72×C11×C13 ⋊ C22 |
| derived | C7×C11×C13 ⋊ C22×C7 |
| Hall | C72×C13 ⋊ C2×D11 |
| Hall | C72×C11 ⋊ C2×D13 |
| Hall | C11×C13 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ D11×D13 |
| Sylow | C13 ⋊ C7×D7×D11 |
| Sylow | C11 ⋊ C7×D7×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D77⋊D13 |
| commutator, cosocle, hypocenter | C7×C11×C13 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11×C13 | C22 |
| LCS | G ▷ C7×C11×C13 | |
| UCS | C1 ◁ C7 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2002 |
1925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28028, 57);