Finite Group DatabasebetaFinite Group Databasebeta| order | 34432 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | D4×Q8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #3538 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D269 |
| commutator, socle, cosocle | C22×C269 | C25 |
| Fitting | D4×Q8×C269 | C2 |
| prime radical | #31771114 | C2 |
| hypercenter | D4×Q8 | D269 |
| hypocenter | C269 | #3538 |
| LCS | G ▷ C22×C269 ▷ C269 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1014 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^7,269|a^2=f,b^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,h^d=h^2683388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34432, 18751);