Finite Group DatabasebetaFinite Group Databasebeta| order | 7068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D57⋊D31 |
| unambiguous semidirect product | D93⋊D19 |
| unambiguous semidirect product | D589⋊D3 |
| Fitting, socle, derived, Hall | C3×C19×C31 ⋊ C22 |
| Hall | C19×C31 ⋊ C2×D3 |
| Hall | C3×C31 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×D31 |
| Sylow | C31 ⋊ D3×D19 |
| Sylow | C19 ⋊ D3×D31 |
| Sylow | C3 ⋊ D19×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C19×C31 | C22 |
| LCS | G ▷ C3×C19×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,19,31|d^a=d^18,e^a=e^30,c^b=c^2,d^b=d^18483 conjugacy classes — view the full character table.
| maximal subgroup of | D171⋊D31, #16812976⋊D3, #16812975⋊D3, … |
| maximal normal subgroup of | #16812976⋊D3, #16812975⋊D3, (C3⋊(D19⋊C3))⋊D31, … |
| maximal quotient of | D171⋊D31, C3×D57⋊D31, D93⋊D57, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7068, 48);