Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic11⋊C25 |
| unambiguous semidirect product | Dic11⋊(C7×C25) |
| unambiguous semidirect product | (C11⋊C25)⋊(C4×C7) |
| unambiguous semidirect product | (C7×Dic11)⋊C25 |
| derived, Sylow | C11 ⋊ C4×C7×C25 |
| Hall | C7×C11⋊C25 ⋊ C4 |
| Hall | C7×Dic11 ⋊ C25 |
| Hall | C11⋊C25 ⋊ C4×C7 |
| Hall | C7×C11 ⋊ C4×C25 |
| Hall | Dic11 ⋊ C7×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C7 | AGL(1,𝔽11) |
| commutator, hypocenter | C11 | C4×C7×C25 |
| Frattini | C2×C5 | C7×AGL(1,𝔽11) |
| Fitting, socle | C2×C5×C7×C11 | C2×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C5×C7 | |
36 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C7×Dic11⋊C25, C7×C3⋊(Dic11⋊C25), ΓL(1,𝔽8)×Dic11⋊C25 |
| maximal normal subgroup of | C3×C7×Dic11⋊C25, ΓL(1,𝔽8)×Dic11⋊C25 |
| maximal quotient of | C3×C7×Dic11⋊C25, C7×C3⋊(Dic11⋊C25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 2);