Finite Group DatabasebetaFinite Group Databasebeta| order | 34432 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×#22575449 |
| Fitting | C23×D4×C269 ⋊ C2 |
| Sylow | C269 ⋊ C22×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D269 |
| commutator, cosocle | C22×C269 | C25 |
| Frattini | C22 | C24×D269 |
| Fitting | C23×D4×C269 | C2 |
| socle | C24×C269 | C23 |
| hypercenter | C23×D4 | D269 |
| hypocenter | C269 | C22×#127 |
| LCS | G ▷ C22×C269 ▷ C269 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
3000 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 725 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 17216 |
5416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34432, 17781);