Finite Group DatabasebetaFinite Group Databasebeta| order | 9375 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C25 · Schur multiplier (H2) = C52 |
| direct product | C3×H(3,𝔽5)⋊C25 |
| unambiguous semidirect product | (C3×H(3,𝔽5))⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C52 | H(3,𝔽5) |
| commutator | C52 | C3×C5×C25 |
| Frattini | C53 | C3×C52 |
| LCS | G ▷ C52 ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C3×C52 ◁ C3×C53 ◁ G | |
150 conjugacy classes of subgroups.
735 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9375, 22);