Finite Group DatabasebetaFinite Group Databasebeta| order | 34432 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #564×C269 ⋊ C2 |
| Sylow | C269 ⋊ #3531 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D269 |
| commutator, socle, cosocle | C22×C269 | C25 |
| Fitting | #564×C269 | C2 |
| hypercenter | #564 | D269 |
| hypocenter | C269 | #3531 |
| LCS | G ▷ C22×C269 ▷ C269 | |
| UCS | C1 ◁ C22 ◁ #564 | |
930 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 451 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^7,269|b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dfg,h^a=h^268,c^b=cfg,d^b=df,h^d=h^268,h^e=h^2682584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34432, 18658);