Finite Group DatabasebetaFinite Group Databasebeta| order | 8435 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C241⋊C5 |
| unambiguous semidirect product | C241⋊(C5×C7) |
| unambiguous semidirect product | (C7×C241)⋊C5 |
| Fitting, socle, Hall | C7×C241 ⋊ C5 |
| derived, Sylow | C241 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C241⋊C5 |
| commutator, hypocenter | C241 | C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C241 | C5 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
371 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C7×C241⋊C5, C7×D241⋊C5, D7×C241⋊C5, … |
| maximal normal subgroup of | C2×C7×C241⋊C5, C7×D241⋊C5, D7×C241⋊C5, … |
| maximal quotient of | C2×C7×C241⋊C5, C3×C7×C241⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8435, 1);