Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | D7×D11×C25 |
| Fitting, Hall | C7×C11×C25 ⋊ C22 |
| derived, Hall | C7×C11 ⋊ C22×C25 |
| Hall | C11×C25 ⋊ C2×D7 |
| Hall | C7×C25 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D7×C25 |
| Sylow | C7 ⋊ C2×D11×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D7×D11 |
| commutator, hypocenter | C7×C11 | C22×C25 |
| Frattini | C5 | C5×D7×D11 |
| Fitting | C7×C11×C25 | C22 |
| socle | C5×C7×C11 | C22×C5 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C25 | |
60 conjugacy classes of subgroups.
875 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C25×AGL(1,𝔽7), C3×D7×D11×C25, D11×C25×D21, … |
| maximal normal subgroup of | D11×C25×AGL(1,𝔽7), C3×D7×D11×C25 |
| maximal quotient of | C3×D7×D11×C25, D11×C25×D21, D7×C25×D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 23);