Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C53 |
| direct product | Q8×C5⋊(C5⋊D5) |
| Fitting | C53×Q8 ⋊ C2 |
| Sylow | C53 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×C5⋊(C5⋊D5) |
| commutator, socle, cosocle | C2×C53 | C23 |
| Fitting | C53×Q8 | C2 |
| prime radical | C2×C5⋊(C5⋊D5) | C22 |
| hypercenter | Q8 | C5⋊(C5⋊D5) |
| hypocenter | C53 | C2×Q8 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
1216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1000 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 888);