Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C22×C5×#1043 |
| Fitting, socle | C22×C53 ⋊ C4 |
| derived | C52 ⋊ C22×C4×C5 |
| Sylow | C53 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | #1043 |
| commutator, hypocenter | C52 | C22×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C53 | C4 |
| prime radical | C22×C5×C5⋊D5 | C2 |
| cosocle | C5⋊D5 | C23×C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C5 | |
492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D5×#1043, C5×#11717375, #72259205, … |
| maximal normal subgroup of | C22×D5×#1043, C5×#11717375, #72259205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 949);