Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×#72213247 |
| Fitting, socle | C22×C34 ⋊ #127 |
| Sylow | C34 ⋊ C22×#127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #72213247 |
| commutator, cosocle | C3⋊D32 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | #127 |
| hypocenter | C34 | C22×#127 |
| LCS | G ▷ C3⋊D32 ▷ C34 | |
| UCS | C1 ◁ C22 | |
14520 conjugacy classes of subgroups; only the 615 normal subgroups are shown.
This group has 14520 conjugacy classes of subgroups — too many to draw. Only its 615 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
168 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.