Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×C11×#1035 |
| Fitting, Hall | C7×C11×C25 ⋊ C4 |
| derived, Sylow | C25 ⋊ C4×C7×C11 |
| Hall | C11×C25 ⋊ C4×C7 |
| Hall | C7×C25 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | #1035 |
| commutator, hypocenter | C25 | C4×C7×C11 |
| Frattini | C5 | C7×C11×AGL(1,𝔽5) |
| Fitting | C7×C11×C25 | C4 |
| socle | C5×C7×C11 | AGL(1,𝔽5) |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C7×C11 | |
36 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | C11×ΓL(1,𝔽8)×#1035, C3×C7×C11×#1035, C7×C11×C3⋊#1035 |
| maximal normal subgroup of | C11×ΓL(1,𝔽8)×#1035, C3×C7×C11×#1035 |
| maximal quotient of | C3×C7×C11×#1035, C7×C11×C3⋊#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 19);