Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11758757 |
| commutator, Fitting, cosocle | C4×C53 | C22 |
| Frattini, hypercenter | C4 | #92566 |
| socle | C2×C53 | D4 |
| hypocenter | C53 | D8 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C4 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^4,5^3|c^2=d,b^a=bc,c^a=cd,e^a=e^4,g^a=g^4,c^b=cd,e^b=e^4,f^b=f^4155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 563);