Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D31×#519 |
| Fitting | C31×#519 ⋊ C2 |
| Sylow | C31 ⋊ C2×#519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D31 |
| commutator | C2×C31 | C24×C4 |
| Fitting | C31×#519 | C2 |
| socle, cosocle | C22×C31 | C25 |
| prime radical | C23×D31 | C23 |
| hypercenter | #519 | D31 |
| hypocenter | C31 | C2×#519 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ #519 | |
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 992 |
578 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 17698);