Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C4×C7×C11⋊C25 |
| unambiguous semidirect product | (C4×C11)⋊(C7×C25) |
| unambiguous semidirect product | (C4×C7×C11)⋊C25 |
| derived, Sylow | C11 ⋊ C4×C7×C25 |
| Hall | C4×C7×C11 ⋊ C25 |
| Hall | C7×C11 ⋊ C4×C25 |
| Hall | C4×C11 ⋊ C7×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5×C7 | C11⋊C5 |
| commutator, hypocenter | C11 | C4×C7×C25 |
| Frattini | C2×C5 | C2×C7×C11⋊C5 |
| Fitting | C4×C5×C7×C11 | C5 |
| socle | C2×C5×C7×C11 | C2×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C4×C5×C7 | |
36 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×C7×C11⋊C25, C4×ΓL(1,𝔽8)×C11⋊C25, C7×Dic3×C11⋊C25 |
| maximal normal subgroup of | C3×C4×C7×C11⋊C25, C4×ΓL(1,𝔽8)×C11⋊C25 |
| maximal quotient of | C3×C4×C7×C11⋊C25, C7×Dic3×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 5);