Finite Group DatabasebetaFinite Group Databasebeta| order | 8060 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D65⋊D31 |
| unambiguous semidirect product | D155⋊D13 |
| unambiguous semidirect product | D403⋊D5 |
| Fitting, socle, derived, Hall | C5×C13×C31 ⋊ C22 |
| Hall | C13×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×D13 |
| Hall | C5×C13 ⋊ C2×D31 |
| Sylow | C31 ⋊ D5×D13 |
| Sylow | C13 ⋊ D5×D31 |
| Sylow | C5 ⋊ D13×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C31 | C22 |
| LCS | G ▷ C5×C13×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,13,31|d^a=d^12,e^a=e^30,c^b=c^4,d^b=d^12542 conjugacy classes — view the full character table.
| maximal subgroup of | #14559031⋊D5, #14559030⋊D5, (C5⋊(D13⋊C3))⋊D31, … |
| maximal normal subgroup of | #14559031⋊D5, #14559030⋊D5, (C5⋊(D13⋊C3))⋊D31, … |
| maximal quotient of | C3×D65⋊D31, D403⋊D15, D155⋊D39, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8060, 39);