Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×#11758752 |
| Sylow | C53 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×C5⋊D5 |
| commutator, cosocle | C2×C53 | C23 |
| Frattini | C2 | C2×D5×C5⋊D5 |
| Fitting, socle | C22×C53 | C22 |
| hypocenter | C53 | C2×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 | |
624 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
218 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 845);