Finite Group DatabasebetaFinite Group Databasebeta| order | 15420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#19104097 |
| Fitting, socle, derived, Hall | C3×C5×C257 ⋊ C4 |
| Hall | C5×C257 ⋊ Dic3 |
| Hall | C3×C257 ⋊ Dic5 |
| Sylow | C257 ⋊ Dic15 |
| Hall | C3×C5 ⋊ #11759967 |
| Sylow | C5 ⋊ C3⋊#11759967 |
| Sylow | C3 ⋊ #19104097 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C257 | C4 |
| prime radical, cosocle | C3×C5×D257 | C2 |
| LCS | G ▷ C3×C5×C257 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3855 |
Polycyclic presentation:
2^2,3,5,257|a^2=b,c^a=c^2,d^a=d^4,e^a=e^241,e^b=e^256978 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15420, 23);