Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic5×C11⋊C5 |
| unambiguous semidirect product | (C11×Dic5)⋊(C5×C7) |
| unambiguous semidirect product | (C7×C11×Dic5)⋊C5 |
| derived | C5×C11 ⋊ C4×C5×C7 |
| Hall | C5×C7×C11⋊C5 ⋊ C4 |
| Hall | C5×C11⋊C5 ⋊ C4×C7 |
| Hall | C7×C11 ⋊ C5×Dic5 |
| Sylow | C11 ⋊ C5×C7×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D5×C11⋊C5 |
| commutator, hypocenter | C5×C11 | C4×C5×C7 |
| Frattini | C2 | C7×D5×C11⋊C5 |
| Fitting, socle | C2×C5×C7×C11 | C2×C5 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C2×C7 | |
64 conjugacy classes of subgroups.
392 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×ΓL(1,𝔽8)×C11⋊C5, C3×C7×Dic5×C11⋊C5, C7×C11⋊C5×Dic15 |
| maximal normal subgroup of | Dic5×ΓL(1,𝔽8)×C11⋊C5, C3×C7×Dic5×C11⋊C5 |
| maximal quotient of | C3×C7×Dic5×C11⋊C5, C7×C11⋊C5×Dic15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 42);