Finite Group DatabasebetaFinite Group Databasebeta| order | 5598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D933 |
| unambiguous semidirect product | C311⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C311 ⋊ C2 |
| Sylow | C311 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C311 | C2 |
| LCS | G ▷ C32×C311 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,311|b^a=b^2,c^a=c^2,d^a=d^3101401 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×D311, D3×D933, C2×C3⋊D933, … |
| maximal normal subgroup of | C3⋊D3×D311, D3×D933, C2×C3⋊D933, … |
| maximal quotient of | C3⋊Dic933, C2×C3⋊D933, C5×C3⋊D933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5598, 10);