Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C53 |
| direct product | C2×C22⋊(C5⋊(C5⋊D5)) |
| unambiguous semidirect product | C23⋊(C5⋊(C5⋊D5)) |
| Fitting | C23×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×C5⋊(C5⋊D5) |
| commutator, cosocle | C2×C53 | C23 |
| Frattini | C2 | C22×C5⋊(C5⋊D5) |
| Fitting | C23×C53 | C2 |
| socle | C22×C53 | C22 |
| hypercenter | C23 | C5⋊(C5⋊D5) |
| hypocenter | C53 | C2×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C23 | |
1728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1000 |
506 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 891);