Finite Group DatabasebetaFinite Group Databasebeta| order | 24870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D829⋊C3 |
| unambiguous semidirect product | D829⋊(C3×C5) |
| unambiguous semidirect product | (C829⋊C3)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D829)⋊C3 |
| Fitting, socle, Hall | C5×C829 ⋊ C2×C3 |
| derived, Sylow | C829 ⋊ C2×C3×C5 |
| Hall | C5×C829⋊C3 ⋊ C2 |
| Hall | C5×D829 ⋊ C3 |
| Hall | C829⋊C3 ⋊ C2×C5 |
| Hall | D829 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D829⋊C3 |
| commutator, cosocle, hypocenter | C829 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C829 | C2×C3 |
| LCS | G ▷ C829 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4145 |
720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24870, 10);