Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D11×D25 |
| unambiguous semidirect product | (C11×D25)⋊(C2×C7) |
| unambiguous semidirect product | (D11×C25)⋊(C2×C7) |
| unambiguous semidirect product | D275⋊(C2×C7) |
| Fitting, Hall | C7×C11×C25 ⋊ C22 |
| derived, Hall | C11×C25 ⋊ C22×C7 |
| Hall | C7×C25 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C7×D11 |
| Sylow | C11 ⋊ C2×C7×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D11×D25 |
| commutator, hypocenter | C11×C25 | C22×C7 |
| Frattini | C5 | C7×D5×D11 |
| Fitting | C7×C11×C25 | C22 |
| socle | C5×C7×C11 | C2×D5 |
| LCS | G ▷ C11×C25 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
686 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×D11×D25, C3×C7×D11×D25, C7×D11×D75, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×D11×D25, C3×C7×D11×D25 |
| maximal quotient of | C3×C7×D11×D25, C7×D11×D75, C7×D25×D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 24);