Finite Group DatabasebetaFinite Group Databasebeta| order | 8260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D5×D59 |
| unambiguous semidirect product | (D5×C59)⋊(C2×C7) |
| unambiguous semidirect product | (C5×D59)⋊(C2×C7) |
| unambiguous semidirect product | D295⋊(C2×C7) |
| Fitting, socle, Hall | C5×C7×C59 ⋊ C22 |
| derived, Hall | C5×C59 ⋊ C22×C7 |
| Hall | C7×C59 ⋊ C2×D5 |
| Sylow | C59 ⋊ C2×C7×D5 |
| Hall | C5×C7 ⋊ C2×D59 |
| Sylow | C5 ⋊ C2×C7×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D5×D59 |
| commutator, hypocenter | C5×C59 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C59 | C22 |
| LCS | G ▷ C5×C59 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
868 conjugacy classes — view the full character table.
| maximal subgroup of | D5×ΓL(1,𝔽8)×D59, C3×C7×D5×D59, C7×D15×D59, … |
| maximal normal subgroup of | D5×ΓL(1,𝔽8)×D59, C3×C7×D5×D59 |
| maximal quotient of | C3×C7×D5×D59, C7×D15×D59, C7×D5×D177, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8260, 15);