Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #1043⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #87855⋊C5 |
| derived | C52 ⋊ C2×C5×C8 |
| Sylow | H(3,𝔽5) ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #1043⋊C5 |
| commutator, hypocenter | C52 | C2×C5×C8 |
| Frattini, socle | C2×C5 | C2×C5×AGL(1,𝔽5) |
| Fitting | C4×H(3,𝔽5) | C4 |
| prime radical | C2×(C5⋊D5)⋊C5 | C4 |
| cosocle | #1039 | C22×C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C4 | |
83 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^2,5,2^2,5^2|a^2=d,b^2=e,d^2=e,f^a=f^2,g^a=g^2,f^c=fg,f^d=f^4,g^d=g^4104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 282);