Finite Group DatabasebetaFinite Group Databasebeta| order | 8556 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D69⋊D31 |
| unambiguous semidirect product | D93⋊D23 |
| unambiguous semidirect product | D713⋊D3 |
| Fitting, socle, derived, Hall | C3×C23×C31 ⋊ C22 |
| Hall | C23×C31 ⋊ C2×D3 |
| Hall | C3×C31 ⋊ C2×D23 |
| Hall | C3×C23 ⋊ C2×D31 |
| Sylow | C31 ⋊ D3×D23 |
| Sylow | C23 ⋊ D3×D31 |
| Sylow | C3 ⋊ D23×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C23×C31 | C22 |
| LCS | G ▷ C3×C23×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,23,31|d^a=d^22,e^a=e^30,c^b=c^2,d^b=d^22579 conjugacy classes — view the full character table.
| maximal subgroup of | D207⋊D31, D69⋊(D31⋊C3), C3×D69⋊D31, … |
| maximal normal subgroup of | D69⋊(D31⋊C3), C3×D69⋊D31 |
| maximal quotient of | D207⋊D31, C3×D69⋊D31, D93⋊D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8556, 24);