Finite Group DatabasebetaFinite Group Databasebeta| order | 24540 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic2045⋊C3 |
| derived, Hall | C5×C409 ⋊ C3×C4 |
| Hall | Dic2045 ⋊ C3 |
| Hall | C5×C409⋊C3 ⋊ C4 |
| Hall | C409⋊C3 ⋊ Dic5 |
| Sylow | C409 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ Dic409⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(D409⋊C3) |
| commutator, hypocenter | C5×C409 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C409 | C2×C3 |
| prime radical | C2×C5×C409⋊C3 | C2 |
| LCS | G ▷ C5×C409 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8180 |
Polycyclic presentation:
2,3,5,409,2|a^2=e,c^a=c^4,d^a=d^408,d^b=d^355704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24540, 12);