Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | AGL(1,𝔽9)×AΓL(1,𝔽9) |
| Fitting, socle, Sylow | C34 ⋊ C8×SD16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator | C32×#157 | C22×C8 |
| Fitting, socle, hypocenter | C34 | C8×SD16 |
| prime radical | C3⋊D3×GO+(4,𝔽2) | C2×C4 |
| cosocle | #1572 | C23 |
| LCS | G ▷ C32×#157 ▷ C32×C3⋊D3 ▷ C34 | |
| UCS | C1 | |
547 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 547 conjugacy classes of subgroups — too many to draw. Only its 64 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.
| maximal subgroup of | AΓL(1,𝔽9)2 |
| maximal normal subgroup of | AΓL(1,𝔽9)2 |
Past the SmallGroups library coverage — no SmallGroups id.