Finite Group DatabasebetaFinite Group Databasebeta| order | 4374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | C3×(#6880⋊C2)⋊C3 |
| Fitting, Sylow | C3×#10624852 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (#6880⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | #733 | C2×C33 |
| Frattini | C3×C9 | C33×D3 |
| Fitting | C3×#10624852 | C2 |
| socle | C32 | #92285 |
| LCS | G ▷ #733 | |
| UCS | C1 ◁ C3 | |
632 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
111 conjugacy classes — view the full character table.
| maximal subgroup of | #72222315 |
Past the SmallGroups library coverage — no SmallGroups id.