Finite Group DatabasebetaFinite Group Databasebeta| order | 24315 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C1621⋊C3 |
| unambiguous semidirect product | (C5×C1621)⋊C3 |
| Fitting, socle, Hall | C5×C1621 ⋊ C3 |
| derived, Sylow | C1621 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C1621⋊C3 |
| commutator, cosocle, hypocenter | C1621 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C1621 | C3 |
| LCS | G ▷ C1621 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8105 |
2715 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24315, 3);