Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of D123 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D123 |
| Fitting, socle | C23×C3×C41 ⋊ C2 |
| derived, Hall | C3×C41 ⋊ C24 |
| Sylow | C41 ⋊ C23×D3 |
| Sylow | C3 ⋊ C23×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D123 |
| commutator, cosocle, hypocenter | C3×C41 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C41 | C2 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C23 | |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 984 |
504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 202);