Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C22×C32 |
| direct product | C22⋊C9×#1094 |
| Sylow | C24 ⋊ C9×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×A42 |
| commutator | C24×C3 | C32×C9 |
| Fitting, prime radical | C24×C33 | C32 |
| socle, cosocle | C24×C32 | C33 |
| hypercenter | C33 | A42 |
| hypocenter | C24 | C9×3−1+2 |
| LCS | G ▷ C24×C3 ▷ C24 | |
| UCS | C1 ◁ C32 ◁ C33 | |
658 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | #10942, #72276569 |
| maximal normal subgroup of | #10942, #72276569 |
Past the SmallGroups library coverage — no SmallGroups id.