Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C5 |
| direct product | D5×C22⋊(C5⋊D5) |
| Fitting | C22×C53 ⋊ C22 |
| Sylow | C53 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×C5⋊D5 |
| commutator, socle, cosocle | C2×C53 | C23 |
| Fitting | C22×C53 | C22 |
| hypercenter | C22 | D5×C5⋊D5 |
| hypocenter | C53 | C2×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C22 | |
624 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 850);