Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #398×C251 ⋊ C2 |
| Sylow | C251 ⋊ #2392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D251 |
| commutator, socle, cosocle | C23×C251 | C24 |
| Fitting | #398×C251 | C2 |
| prime radical | #30631597 | C2 |
| hypercenter | #398 | D251 |
| hypocenter | C251 | #2392 |
| LCS | G ▷ C23×C251 ▷ C251 | |
| UCS | C1 ◁ C23 ◁ #398 | |
696 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 16064 |
Polycyclic presentation:
2^7,251|a^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^250,h^c=h^250,h^d=h^2502794 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 7751);