Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D31×#576 |
| Fitting | C31×#576 ⋊ C2 |
| Sylow | C31 ⋊ C2×#576 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D31 |
| commutator, cosocle | C4×C31 | C25 |
| Frattini | C4 | C24×D31 |
| Fitting | C31×#576 | C2 |
| socle | C2×C31 | C23×D4 |
| hypercenter | #576 | D31 |
| hypocenter | C31 | C2×#576 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #576 | |
1512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
374 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 19258);