Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C31×#519 ⋊ C2 |
| Sylow | C31 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D31 |
| commutator | C2×C31 | C24×C4 |
| Fitting | C31×#519 | C2 |
| socle, cosocle | C22×C31 | C25 |
| prime radical | C22×#92499 | C2 |
| hypercenter | #519 | D31 |
| hypocenter | C31 | #3428 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ #519 | |
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^7,31|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^b=h^30,h^c=h^30,h^e=h^30578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 17712);