Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C24×C33 |
| direct product | C3⋊(C3⋊D3)×#1020 |
| Fitting, socle | C24×C33 ⋊ C2×D3 |
| derived | C33×C22⋊A4 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33×C22⋊A4 | C22 |
| Fitting, socle | C24×C33 | C2×D3 |
| LCS | G ▷ C33×C22⋊A4 | |
| UCS | C1 | |
7522 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 7522 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
150 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×#1020, #72220866 |
| maximal normal subgroup of | D3×C3⋊D3×#1020, #72220866 |
Past the SmallGroups library coverage — no SmallGroups id.