Finite Group DatabasebetaFinite Group Databasebeta| order | 31284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊(D79⋊C3) |
| unambiguous semidirect product | (C3⋊(D79⋊C3))⋊D11 |
| unambiguous semidirect product | (C11⋊(D79⋊C3))⋊D3 |
| unambiguous semidirect product | (D33⋊D79)⋊C3 |
| Fitting, socle, derived | C3×C11×C79 ⋊ C22×C3 |
| Hall | C3×C11×C79⋊C3 ⋊ C22 |
| Hall | C11×C79 ⋊ C2×C3×D3 |
| Hall | C3×C79⋊C3 ⋊ C2×D11 |
| Sylow | C79 ⋊ C3×D3×D11 |
| Sylow | C11 ⋊ D3×D79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C79 | C22×C3 |
| LCS | G ▷ C3×C11×C79 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2607 |
Polycyclic presentation:
2^2,3^2,11,79|e^a=e^10,f^a=f^78,d^b=d^2,e^b=e^10,f^c=f^23297 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31284, 61);