Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C3⋊#64188 |
| derived | C3×C22⋊(C22⋊C9) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊#64188 |
| commutator, cosocle, hypocenter | C3×C22⋊(C22⋊C9) | C23 |
| Frattini | C3 | C22×C3⋊#1020 |
| Fitting, socle | C26×C32 | D3 |
| LCS | G ▷ C3×C22⋊(C22⋊C9) | |
| UCS | C1 ◁ C22 | |
8392 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 8392 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72220146, C22×#72220148 |
| maximal normal subgroup of | C22×#72220148 |
Past the SmallGroups library coverage — no SmallGroups id.