Finite Group DatabasebetaFinite Group Databasebeta| order | 7575 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×#14579003 |
| derived, Sylow | C101 ⋊ C3×C25 |
| Hall | C3×C101 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C101⋊C5 |
| commutator, hypocenter | C101 | C3×C25 |
| Frattini | C5 | C3×C101⋊C5 |
| Fitting, socle | C3×C5×C101 | C5 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C3×C5 | |
12 conjugacy classes of subgroups.
375 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7575, 2);