Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5×C25 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×D25 |
| commutator | C2×C5×C25 | C2×C4 |
| Frattini | C22×C5 | D52 |
| Fitting, cosocle | C22×C5×C25 | C22 |
| socle, prime radical | C22×C52 | C2×D5 |
| hypocenter | C5×C25 | C4⋊C4 |
| LCS | G ▷ C2×C5×C25 ▷ C5×C25 | |
| UCS | C1 ◁ C22 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^4,5^3|a^2=d,b^2=d,f^5=g,b^a=bc,f^a=f^4g^4,g^a=g^4,e^b=e^4218 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 104);