Finite Group DatabasebetaFinite Group Databasebeta| order | 23730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C113 · Schur multiplier (H2) = C1 |
| direct product | C3×D35×C113 |
| unambiguous semidirect product | C5⋊(C3×D7×C113) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C113 | D35 |
| commutator, cosocle, hypocenter | C5×C7 | C2×C3×C113 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C113 | C2 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C3×C113 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11865 |
6441 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23730, 9);