Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23×C32 |
| direct product | C3⋊S42 |
| Fitting, socle | C24×C32 ⋊ D32 |
| derived | C32×A42 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×A42 | C22 |
| Fitting, socle | C24×C32 | D32 |
| LCS | G ▷ C32×A42 | |
| UCS | C1 | |
2527 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 2527 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
81 conjugacy classes — view the full character table.
| maximal subgroup of | #72222968, #72222976, #72222979, … |
| maximal normal subgroup of | #72222968, #72222979, D3×S4×C3⋊S4 |
Past the SmallGroups library coverage — no SmallGroups id.