Finite Group DatabasebetaFinite Group Databasebeta| order | 30310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D3031 |
| unambiguous semidirect product | C7⋊(C5×D433) |
| unambiguous semidirect product | C433⋊(C5×D7) |
| Fitting, socle, Hall | C5×C7×C433 ⋊ C2 |
| derived, Hall | C7×C433 ⋊ C2×C5 |
| Hall | C5×C433 ⋊ D7 |
| Sylow | C433 ⋊ C5×D7 |
| Hall | C5×C7 ⋊ D433 |
| Sylow | C7 ⋊ C5×D433 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3031 |
| commutator, cosocle, hypocenter | C7×C433 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C433 | C2 |
| LCS | G ▷ C7×C433 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15155 |
7585 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30310, 4);