Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #92538 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×#11758648 |
| derived, Sylow | C5×C25 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92538 |
| commutator, hypocenter | C5×C25 | C2×C8 |
| Frattini | C2×C5 | C2×#1044 |
| Fitting | C22×C5×C25 | C4 |
| socle, prime radical | C22×C52 | AGL(1,𝔽5) |
| cosocle | #92524 | C22 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 ◁ C22 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 345);