Finite Group DatabasebetaFinite Group Databasebeta| order | 6975 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C9×C31⋊C25 |
| unambiguous semidirect product | (C9×C31)⋊C25 |
| derived, Sylow | C31 ⋊ C9×C25 |
| Hall | C9×C31 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C9 | ΓL(1,𝔽32) |
| commutator, hypocenter | C31 | C9×C25 |
| Frattini | C3×C5 | C3×ΓL(1,𝔽32) |
| Fitting | C5×C9×C31 | C5 |
| socle | C3×C5×C31 | C3×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C9 | |
18 conjugacy classes of subgroups.
495 conjugacy classes — view the full character table.
| maximal subgroup of | C9×D31⋊C25, D9×C31⋊C25, C9⋊(D31⋊C25), … |
| maximal normal subgroup of | C9×D31⋊C25, D9×C31⋊C25, C9⋊(D31⋊C25), … |
| maximal quotient of | C2×C9×C31⋊C25, C22⋊C9×C31⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6975, 3);