Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Sylow | C53 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×C5⋊D5 |
| commutator, socle, cosocle | C2×C53 | C23 |
| Fitting | C4×C53 | C22 |
| prime radical | C2×C5⋊(C5⋊D5) | C22 |
| hypercenter | C4 | D5×C5⋊D5 |
| hypocenter | C53 | C2×Q8 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C4 | |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^4,5^3|a^2=d,b^2=d,c^2=d,c^a=cd,e^a=e^4,f^a=f^4,c^b=cd,g^b=g^4176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 831);