Finite Group DatabasebetaFinite Group Databasebeta| order | 23030 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47×C49 · Schur multiplier (H2) = C1 |
| direct product | D5×C47×C49 |
| unambiguous semidirect product | C5⋊(C2×C47×C49) |
| Fitting, Hall | C5×C47×C49 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C47×C49 |
| Hall | C5×C49 ⋊ C2×C47 |
| Hall | C5×C47 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47×C49 | D5 |
| commutator, hypocenter | C5 | C2×C47×C49 |
| Frattini | C7 | C7×D5×C47 |
| Fitting | C5×C47×C49 | C2 |
| socle | C5×C7×C47 | C2×C7 |
| prime radical | C7×D5×C47 | C7 |
| cosocle | C5×C7 | C2×C7×C47 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C47×C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11515 |
9212 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23030, 5);