Finite Group DatabasebetaFinite Group Databasebeta| order | 24540 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic409⋊C3 |
| unambiguous semidirect product | Dic409⋊(C3×C5) |
| unambiguous semidirect product | (C5×Dic409)⋊C3 |
| derived, Sylow | C409 ⋊ C3×C4×C5 |
| Hall | C5×Dic409 ⋊ C3 |
| Hall | C5×C409⋊C3 ⋊ C4 |
| Hall | C5×C409 ⋊ C3×C4 |
| Hall | Dic409 ⋊ C3×C5 |
| Hall | C409⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D409⋊C3 |
| commutator, hypocenter | C409 | C3×C4×C5 |
| Frattini | C2 | C5×D409⋊C3 |
| Fitting, socle | C2×C5×C409 | C2×C3 |
| prime radical | C2×C5×C409⋊C3 | C2 |
| cosocle | C2×C409 | C2×C3×C5 |
| LCS | G ▷ C409 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8180 |
740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24540, 10);