Finite Group DatabasebetaFinite Group Databasebeta| order | 24540 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #22551126⋊C3 |
| Fitting, socle, derived, Hall | C5×C409 ⋊ C3×C4 |
| Hall | #22551126 ⋊ C3 |
| Hall | C5×C409⋊C3 ⋊ C4 |
| Hall | C409⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C409 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic409⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C409 | C3×C4 |
| prime radical | D5×C409⋊C3 | C2 |
| cosocle | D5×C409 | C2×C3 |
| LCS | G ▷ C5×C409 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2045 |
Polycyclic presentation:
2,3,2,5,409|a^2=c,d^a=d^2,e^a=e^408,e^b=e^53,d^c=d^4287 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24540, 17);