Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C53 |
No aliases for this group.
| Fitting | C53×Q8 ⋊ C2 |
| Sylow | C53 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×C5⋊(C5⋊D5) |
| commutator, socle, cosocle | C2×C53 | C23 |
| Fitting | C53×Q8 | C2 |
| hypercenter | Q8 | C5⋊(C5⋊D5) |
| hypocenter | C53 | #41 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
1280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1000 |
Polycyclic presentation:
2^4,5^3|b^2=d,c^2=d,c^a=cd,e^a=e^4,f^a=f^4,g^a=g^4,c^b=cd320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 889);