Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C251 ⋊ #2811 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D251 |
| commutator, socle, prime radical, cosocle | C23×C251 | C24 |
| Fitting | #391×C251 | C2 |
| hypercenter | #391 | D251 |
| hypocenter | C251 | #2811 |
| LCS | G ▷ C23×C251 ▷ C251 | |
| UCS | C1 ◁ C23 ◁ #391 | |
432 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 32128 |
Polycyclic presentation:
2^7,251|a^2=ef,b^2=eg,c^2=fg,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^c=h^2503532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 12503);