Finite Group DatabasebetaFinite Group Databasebeta| order | 8365 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C239⋊C7 |
| unambiguous semidirect product | C239⋊(C5×C7) |
| unambiguous semidirect product | (C5×C239)⋊C7 |
| Fitting, socle, Hall | C5×C239 ⋊ C7 |
| derived, Sylow | C239 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C239⋊C7 |
| commutator, hypocenter | C239 | C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C239 | C7 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
205 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×C239⋊C7, C5×D239⋊C7, D5×C239⋊C7, … |
| maximal normal subgroup of | C2×C5×C239⋊C7, C5×D239⋊C7, D5×C239⋊C7, … |
| maximal quotient of | C2×C5×C239⋊C7, C3×C5×C239⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8365, 1);