Finite Group DatabasebetaFinite Group Databasebeta| order | 9375 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C53 |
| direct product | C52⋊C3×H(3,𝔽5) |
| unambiguous semidirect product | (C52×C52⋊C3)⋊C5 |
| Fitting, Sylow | C52×H(3,𝔽5) ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C52×C52⋊C3 |
| commutator, socle | C53 | C3×C52 |
| Fitting | C52×H(3,𝔽5) | C3 |
| hypercenter | H(3,𝔽5) | C52⋊C3 |
| hypocenter | C52 | C3×H(3,𝔽5) |
| LCS | G ▷ C53 ▷ C52 | |
| UCS | C1 ◁ C5 ◁ H(3,𝔽5) | |
842 conjugacy classes of subgroups.
319 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9375, 94);