Finite Group DatabasebetaFinite Group Databasebeta| order | 28908 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×#10620323⋊C2 |
| unambiguous semidirect product | #10620323⋊(C22×C11) |
| unambiguous semidirect product | (C2×#10620323)⋊(C2×C11) |
| Fitting, socle | C2×C11×C73 ⋊ C2×C9 |
| derived, Sylow | C73 ⋊ C22×C9×C11 |
| Hall | C11×#10620323 ⋊ C22 |
| Hall | C2×C11×D73 ⋊ C9 |
| Hall | C11×C73 ⋊ C22×C9 |
| Hall | #10620323 ⋊ C22×C11 |
| Hall | C2×D73 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | #10620323⋊C2 |
| commutator, hypocenter | C73 | C22×C9×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C73 | C2×C9 |
| prime radical | C2×C11×D73⋊C3 | C3 |
| cosocle | C73⋊C3 | C22×C3×C11 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C11 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1606 |
484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28908, 69);