Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D53 |
| unambiguous semidirect product | (D5×C5⋊D5)⋊C22 |
| Fitting, socle | C2×C53 ⋊ C23 |
| derived, Sylow | C53 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D53 |
| commutator, cosocle, hypocenter | C53 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C2×C53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
768 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#87886, D5×#87831, C2×D5×D5⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | D5×#87886, D5×#87831, C2×D5×D5⋊AGL(1,𝔽5), … |
| maximal quotient of | D5×#87886, C2×D5×#6036 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 946);