Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D77⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C7×C11 ⋊ C22 |
| Hall | C52×C11 ⋊ C2×D7 |
| Hall | C52×C7 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ D7×D11 |
| Sylow | C11 ⋊ D7×C5⋊D5 |
| Sylow | C7 ⋊ D11×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7×C11 | C22 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,7,11|e^a=e^6,f^a=f^10,c^b=c^4,d^b=d^4,e^b=e^6515 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 105);