Finite Group DatabasebetaFinite Group Databasebeta| order | 24060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#13107944⋊C5) |
| unambiguous semidirect product | (C3⋊#13107944)⋊C5 |
| Fitting, socle, derived, Hall | C3×C401 ⋊ C4×C5 |
| Hall | C3×C401⋊C5 ⋊ C4 |
| Hall | C3⋊#13107944 ⋊ C5 |
| Hall | C401⋊C5 ⋊ Dic3 |
| Sylow | C401 ⋊ C5×Dic3 |
| Sylow | C3 ⋊ #13107944⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C401 | C4×C5 |
| prime radical | C3×D401⋊C5 | C2 |
| cosocle | C3×D401 | C2×C5 |
| LCS | G ▷ C3×C401 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1203 |
Polycyclic presentation:
2,5,2,3,401|a^2=c,d^a=d^2,e^a=e^20,e^b=e^72,e^c=e^40090 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24060, 15);