Finite Group DatabasebetaFinite Group Databasebeta| order | 8260 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C59 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D7×C59 |
| unambiguous semidirect product | C7⋊(C22×C5×C59) |
| unambiguous semidirect product | (C2×C7)⋊(C2×C5×C59) |
| Fitting, socle | C2×C5×C7×C59 ⋊ C2 |
| derived, Sylow | C7 ⋊ C22×C5×C59 |
| Hall | C5×C7×C59 ⋊ C22 |
| Hall | C7×C59 ⋊ C22×C5 |
| Hall | C5×C7 ⋊ C22×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C59 | D7 |
| commutator, hypocenter | C7 | C22×C5×C59 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C59 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C5×C59 | |
40 conjugacy classes of subgroups.
2950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×AGL(1,𝔽7)×C59, C5×D3×D7×C59, C2×C3×C5×D7×C59, … |
| maximal normal subgroup of | C2×C5×AGL(1,𝔽7)×C59, C2×C3×C5×D7×C59 |
| maximal quotient of | C5×D3×D7×C59, C2×C3×C5×D7×C59, C2×C5×D21×C59 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8260, 26);