Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | AΓL(1,𝔽9)2 |
| Fitting, socle, Sylow | C34 ⋊ SD162 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | #1572 | C24 |
| Fitting, socle, hypocenter | C34 | SD162 |
| prime radical | GO+(4,𝔽2)2 | C22 |
| LCS | G ▷ #1572 ▷ C3⋊D32 ▷ C34 | |
| UCS | C1 | |
2175 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 2175 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 81 |
81 conjugacy classes — view the full character table.
| holomorph of | AΓL(1,𝔽9) |
Past the SmallGroups library coverage — no SmallGroups id.