Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #92535 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×#11758645 |
| derived, Sylow | H(3,𝔽5) ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92535 |
| commutator, hypocenter | H(3,𝔽5) | C2×C8 |
| Frattini | C2×C5 | C2×#1042 |
| Fitting, prime radical | C22×H(3,𝔽5) | C4 |
| socle | C22×C5 | #1042 |
| cosocle | #1039⋊C5 | C22 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C22 | |
87 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 320);