Finite Group DatabasebetaFinite Group Databasebeta| order | 23030 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C49 · Schur multiplier (H2) = C1 |
| direct product | C5×C49×D47 |
| unambiguous semidirect product | C47⋊(C2×C5×C49) |
| Fitting, Hall | C5×C47×C49 ⋊ C2 |
| derived, Sylow | C47 ⋊ C2×C5×C49 |
| Hall | C47×C49 ⋊ C2×C5 |
| Hall | C5×C47 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C49 | D47 |
| commutator, hypocenter | C47 | C2×C5×C49 |
| Frattini | C7 | C5×C7×D47 |
| Fitting | C5×C47×C49 | C2 |
| socle | C5×C7×C47 | C2×C7 |
| prime radical | C5×C7×D47 | C7 |
| cosocle | C7×C47 | C2×C5×C7 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C5×C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11515 |
6125 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23030, 2);