Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C31×#342 ⋊ C2 |
| Sylow | C31 ⋊ #2021 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #11758459 |
| commutator, cosocle | C24×C31 | C23 |
| Frattini | C24 | C22×D31 |
| Fitting | C31×#342 | C2 |
| socle | C22×C31 | #120 |
| hypercenter | #342 | D31 |
| hypocenter | C31 | #2021 |
| LCS | G ▷ C24×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #342 | |
638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^7,31|b^a=bd,c^a=ce,f^a=fg,h^a=h^30,c^b=cf,h^b=h^30,d^c=dg,h^c=h^30356 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 5637);