Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D5×D52⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D5×D52⋊C2 |
| unambiguous semidirect product | D53⋊C2 |
| Fitting, socle, Sylow | C53 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C5×C5⋊D5 | C23 |
| Fitting, socle, hypocenter | C53 | C2×D4 |
| LCS | G ▷ C5×C5⋊D5 ▷ C53 | |
| UCS | C1 | |
232 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 20 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 919);