Finite Group DatabasebetaFinite Group Databasebeta| order | 5832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | D3×#11757731 |
| Fitting, derived, Sylow | C3×C32⋊H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C32⋊H(3,𝔽3) | C23 |
| Frattini | C32 | D32×C3⋊D3 |
| socle | C33 | C2×D3×C3⋊D3 |
| LCS | G ▷ C3×C32⋊H(3,𝔽3) | |
| UCS | C1 | |
3493 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 3493 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72210292, D3×((((C3⋊D3)⋊C3)⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | D3×((((C3⋊D3)⋊C3)⋊D3)⋊C3)⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.