Finite Group DatabasebetaFinite Group Databasebeta| order | 5415 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #11762245⋊C5 |
| unambiguous semidirect product | (C192⋊C5)⋊C3 |
| Fitting, socle, derived, Sylow | C192 ⋊ C3×C5 |
| Hall | C192⋊C5 ⋊ C3 |
| Hall | #11762245 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C192 | C3×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,19^2|c^a=c^11,d^a=d^11,c^b=c^12d^8,d^b=c^14d^1139 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5415, 4);