Finite Group DatabasebetaFinite Group Databasebeta| order | 2808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#10622027⋊C2 |
| Fitting | C2×C9×C13 ⋊ C22×C3 |
| derived | C9×C13 ⋊ C23×C3 |
| Hall | #66849 ⋊ C23 |
| Sylow | C13 ⋊ C22×AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10622027⋊C2 |
| commutator, cosocle, hypocenter | C9×C13 | C23×C3 |
| Frattini | C3 | C2×D3×D13⋊C3 |
| Fitting | C2×C9×C13 | C22×C3 |
| socle | C2×C3×C13 | C2×C3×D3 |
| LCS | G ▷ C9×C13 | |
| UCS | C1 ◁ C2 | |
202 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 234 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72228967, C2×AGL(1,ℤ/9)×D13⋊C3 |
| maximal normal subgroup of | C2×#72228967, C2×AGL(1,ℤ/9)×D13⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.