Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5×C25 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11758656 |
| commutator, Fitting, cosocle | C4×C5×C25 | C22 |
| Frattini | C4×C5 | D52 |
| socle | C2×C52 | C22⋊D5 |
| hypercenter | C4 | D5×D25 |
| hypocenter | C5×C25 | D8 |
| LCS | G ▷ C4×C5×C25 ▷ C2×C5×C25 ▷ C5×C25 | |
| UCS | C1 ◁ C2 ◁ C4 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^4,5^3|b^2=cd,c^2=d,e^5=g,b^a=bc,c^a=cd,f^a=f^4,e^b=e^4g^4,g^b=g^4179 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 84);