Finite Group DatabasebetaFinite Group Databasebeta| order | 8260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D413 |
| unambiguous semidirect product | (C2×C7)⋊(C5×D59) |
| unambiguous semidirect product | (C2×C59)⋊(C5×D7) |
| Fitting, socle | C2×C5×C7×C59 ⋊ C2 |
| derived, Hall | C7×C59 ⋊ C22×C5 |
| Hall | C5×C7×C59 ⋊ C22 |
| Hall | C5×C59 ⋊ C2×D7 |
| Sylow | C59 ⋊ C2×C5×D7 |
| Hall | C5×C7 ⋊ C2×D59 |
| Sylow | C7 ⋊ C2×C5×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D413 |
| commutator, hypocenter | C7×C59 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C59 | C2 |
| LCS | G ▷ C7×C59 | |
| UCS | C1 ◁ C2×C5 | |
40 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×ΓL(1,𝔽8)⋊D59, C5×D3×D413, C2×C3×C5×D413, … |
| maximal normal subgroup of | C2×C5×ΓL(1,𝔽8)⋊D59, C2×C3×C5×D413 |
| maximal quotient of | C5×D3×D413, C2×C3×C5×D413, C2×C5×D1239 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8260, 25);