Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C251 ⋊ #2320 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D251 |
| commutator | C22×C251 | C23×C4 |
| Fitting | #382×C251 | C2 |
| socle, prime radical, cosocle | C23×C251 | C24 |
| hypercenter | #382 | D251 |
| hypocenter | C251 | #2320 |
| LCS | G ▷ C22×C251 ▷ C251 | |
| UCS | C1 ◁ C23 ◁ #382 | |
444 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32128 |
Polycyclic presentation:
2^7,251|a^2=g,b^2=e,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^2503544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 7158);