Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C5 |
| direct product | #170×C5⋊D5 |
| derived, Sylow | C53 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×C5⋊D5 |
| commutator, hypocenter | C53 | C2×C8 |
| Fitting, socle | C2×C53 | C2×C4 |
| prime radical | C2×C5×C5⋊D5 | C4 |
| cosocle | C52×Dic5 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 687);