Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×#11724050 |
| derived | C22⋊(C22⋊C9) ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11724050 |
| commutator, cosocle, hypocenter | C22⋊(C22⋊C9) | C23×C3 |
| Frattini | C3 | C22×C3×#1020 |
| Fitting | C26×C32 | D3 |
| socle | C26×C3 | C3×D3 |
| LCS | G ▷ C22⋊(C22⋊C9) | |
| UCS | C1 ◁ C22 | |
6503 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 6503 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213207, C22×#72220148, C22×#72220155 |
| maximal quotient of | #72253113, C22×#72220148 |
Past the SmallGroups library coverage — no SmallGroups id.