Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D40 |
| Fitting | C53×C8 ⋊ C2 |
| Sylow | C53 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C52 | D20 |
| commutator, cosocle | C4×C5 | C22×C52 |
| Frattini | C4 | C2×C52×D5 |
| Fitting | C53×C8 | C2 |
| socle | C2×C53 | D4 |
| hypercenter | C52×C8 | D5 |
| hypocenter | C5 | C52×D8 |
| LCS | G ▷ C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C52 ◁ C4×C52 ◁ C52×C8 | |
272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
575 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 572);