Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#72219716 |
| Sylow | C34 ⋊ C2×#120 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #13049813 |
| commutator, cosocle | C2×C3⋊(C3⋊(C3⋊D3)) | C24 |
| Frattini | C2 | C2×#13049813 |
| Fitting, socle | C22×C34 | C2×D4 |
| hypocenter | C34 | C2×#120 |
| LCS | G ▷ C2×C3⋊(C3⋊(C3⋊D3)) ▷ C34 | |
| UCS | C1 ◁ C22 | |
5936 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 5936 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
120 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.