Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic275 |
| unambiguous semidirect product | C11⋊(C7×Dic25) |
| derived, Hall | C11×C25 ⋊ C4×C7 |
| Hall | C7×C11×C25 ⋊ C4 |
| Hall | C7×C25 ⋊ Dic11 |
| Hall | C7×C11 ⋊ Dic25 |
| Sylow | C25 ⋊ C7×Dic11 |
| Sylow | C11 ⋊ C7×Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D275 |
| commutator, hypocenter | C11×C25 | C4×C7 |
| Frattini | C2×C5 | C7×D55 |
| Fitting | C2×C7×C11×C25 | C2 |
| socle | C2×C5×C7×C11 | D5 |
| LCS | G ▷ C11×C25 | |
| UCS | C1 ◁ C2×C7 | |
36 conjugacy classes of subgroups.
1946 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×Dic275, C7×Dic825, ΓL(1,𝔽8)×Dic275 |
| maximal normal subgroup of | C3×C7×Dic275, ΓL(1,𝔽8)×Dic275 |
| maximal quotient of | C3×C7×Dic275, C7×Dic825 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 10);