Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D5×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C5 |
| direct product | C22×D5×C5⋊D5 |
| Fitting, socle | C22×C53 ⋊ C22 |
| derived, Sylow | C53 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×C5⋊D5 |
| commutator, cosocle, hypocenter | C53 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C53 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22 | |
1456 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1456 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D5×#1043, C22×AGL(1,𝔽5)×C5⋊D5, C22×D5⋊#1043, … |
| maximal normal subgroup of | C22×D5×#1043, C22×AGL(1,𝔽5)×C5⋊D5, C22×D5⋊#1043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 958);