Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D5×#1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | Dic5×#1042 |
| derived, Sylow | C53 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×#1042 |
| commutator, hypocenter | C53 | C42 |
| Fitting, socle | C2×C53 | C2×C4 |
| prime radical, cosocle | C2×C52×D5 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
172 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#6036, #72259432, #72259439, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#6036, #72259432, #72259439, … |
| maximal quotient of | C2×Dic5×#1042 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 691);