Finite Group DatabasebetaFinite Group Databasebeta| order | 9025 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C192⋊C25 |
| derived, Sylow | C192 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C192⋊C5 |
| commutator, hypocenter | C192 | C25 |
| Fitting, socle | C5×C192 | C5 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C5 | |
14 conjugacy classes of subgroups.
Polycyclic presentation:
5,19^2,5|a^5=d,b^a=b^12c^18,c^a=b^2c^11385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9025, 4);