Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#14521744 |
| Fitting | C2×C31×#123 ⋊ C2 |
| Sylow | C31 ⋊ C2×#553 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D31 |
| commutator, cosocle | C22×C31 | C25 |
| Frattini | C22 | C24×D31 |
| Fitting | C2×C31×#123 | C2 |
| socle | C23×C31 | C24 |
| hypercenter | C2×#123 | D31 |
| hypocenter | C31 | C2×#553 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1984 |
470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 18028);