Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C52 · Schur multiplier (H2) = C23×C5 |
| direct product | C52×D4×D5 |
| Fitting | C53×D4 ⋊ C2 |
| Sylow | C53 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C52 | C22×D5 |
| commutator, cosocle | C2×C5 | C23×C52 |
| Frattini | C2 | C22×C52×D5 |
| Fitting | C53×D4 | C2 |
| socle | C2×C53 | C23 |
| hypercenter | C52×D4 | D5 |
| hypocenter | C5 | C2×C52×D4 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C52 ◁ C52×D4 | |
624 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 866);