Finite Group DatabasebetaFinite Group Databasebeta| order | 30276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D292 |
| unambiguous semidirect product | (C29×D29)⋊(C2×C9) |
| Fitting, Hall | C9×C292 ⋊ C22 |
| derived, Sylow | C292 ⋊ C22×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D292 |
| commutator, hypocenter | C292 | C22×C9 |
| Frattini | C3 | C3×D292 |
| Fitting | C9×C292 | C22 |
| socle, cosocle | C3×C292 | C22×C3 |
| prime radical | C3×D292 | C3 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C9 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 522 |
2304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30276, 56);