Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #92566 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#92566 |
| Fitting, socle | C22×C53 ⋊ C22 |
| derived, Sylow | C53 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92566 |
| commutator, cosocle, hypocenter | C53 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C53 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22 | |
768 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 959);