Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #87837 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#87839 |
| Sylow | C53 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D52⋊C2 |
| commutator, cosocle | #1039 | C22×C5 |
| Frattini | C2 | C5×D52⋊C2 |
| Fitting, socle, prime radical | C2×C53 | D4 |
| hypocenter | C52 | C5×Q16 |
| LCS | G ▷ #1039 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
125 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 709);