Finite Group DatabasebetaFinite Group Databasebeta| order | 24230 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2423 |
| unambiguous semidirect product | C2423⋊(C2×C5) |
| Fitting, socle, Hall | C5×C2423 ⋊ C2 |
| derived, Sylow | C2423 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2423 |
| commutator, cosocle, hypocenter | C2423 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C2423 | C2 |
| LCS | G ▷ C2423 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12115 |
6065 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24230, 2);