Finite Group DatabasebetaFinite Group Databasebeta| order | 8670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C17 |
| direct product | C2×C5×C172⋊C3 |
| unambiguous semidirect product | (C2×C172)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×C172)⋊C3 |
| Fitting, socle, Hall | C2×C5×C172 ⋊ C3 |
| derived, Sylow | C172 ⋊ C2×C3×C5 |
| Hall | C5×C172 ⋊ C2×C3 |
| Hall | C2×C172 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C172⋊C3 |
| commutator, hypocenter | C172 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C172 | C3 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C2×C5 | |
40 conjugacy classes of subgroups.
990 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#16812392, C5×#11923880⋊C3, #31773227, … |
| maximal normal subgroup of | C5×#16812392, C5×#11923880⋊C3, #31773227, … |
| maximal quotient of | C4×C5×C172⋊C3, C22×C5×C172⋊C3, C2×C5×#14579583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8670, 15);