Finite Group DatabasebetaFinite Group Databasebeta| order | 8260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D35⋊D59 |
| unambiguous semidirect product | D295⋊D7 |
| unambiguous semidirect product | D413⋊D5 |
| Fitting, socle, derived, Hall | C5×C7×C59 ⋊ C22 |
| Hall | C7×C59 ⋊ C2×D5 |
| Hall | C5×C59 ⋊ C2×D7 |
| Sylow | C59 ⋊ D5×D7 |
| Hall | C5×C7 ⋊ C2×D59 |
| Sylow | C7 ⋊ D5×D59 |
| Sylow | C5 ⋊ D7×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C59 | C22 |
| LCS | G ▷ C5×C7×C59 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,7,59|d^a=d^6,e^a=e^58,c^b=c^4,d^b=d^6571 conjugacy classes — view the full character table.
| maximal subgroup of | (C5⋊AGL(1,𝔽7))⋊D59, C3×D35⋊D59, D413⋊D15, … |
| maximal normal subgroup of | (C5⋊AGL(1,𝔽7))⋊D59, C3×D35⋊D59 |
| maximal quotient of | C3×D35⋊D59, D413⋊D15, D295⋊D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8260, 20);