Finite Group DatabasebetaFinite Group Databasebeta| order | 32896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C257 ⋊ #2295 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D257 |
| commutator | C22×C257 | C23×C4 |
| Fitting | #389×C257 | C2 |
| socle, prime radical, cosocle | C23×C257 | C24 |
| hypercenter | #389 | D257 |
| hypocenter | C257 | #2295 |
| LCS | G ▷ C22×C257 ▷ C257 | |
| UCS | C1 ◁ C23 ◁ #389 | |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32896 |
Polycyclic presentation:
2^7,257|a^2=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,h^d=h^2563640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32896, 6981);