Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| isoclinism | isoclinic class of D77 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×Dic77 |
| unambiguous semidirect product | C7⋊(C25×Dic11) |
| derived, Hall | C7×C11 ⋊ C4×C25 |
| Hall | C7×C11×C25 ⋊ C4 |
| Hall | C11×C25 ⋊ Dic7 |
| Hall | C7×C25 ⋊ Dic11 |
| Sylow | C11 ⋊ C25×Dic7 |
| Sylow | C7 ⋊ C25×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D77 |
| commutator, hypocenter | C7×C11 | C4×C25 |
| Frattini | C2×C5 | C5×D77 |
| Fitting | C2×C7×C11×C25 | C2 |
| socle | C2×C5×C7×C11 | C2×C5 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C2×C25 | |
36 conjugacy classes of subgroups.
2000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C25×Dic77, C25×Dic231, C25×C11⋊(ΓL(1,𝔽8)⋊C4) |
| maximal normal subgroup of | C3×C25×Dic77, C25×C11⋊(ΓL(1,𝔽8)⋊C4) |
| maximal quotient of | C3×C25×Dic77, C25×Dic231 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 8);