Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C52 · Schur multiplier (H2) = C22×C5 |
| direct product | C52×#713 |
| Fitting | C53×Q8 ⋊ C2 |
| Sylow | C53 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C52 | C22×D5 |
| commutator, cosocle | C2×C5 | C23×C52 |
| Frattini | C2 | C22×C52×D5 |
| Fitting | C53×Q8 | C2 |
| socle | C2×C53 | C23 |
| hypercenter | C52×Q8 | D5 |
| hypocenter | C5 | C52×#41 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C52 ◁ C52×Q8 | |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 869);