Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| derived, Sylow | C53 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D53 |
| commutator, hypocenter | C53 | C22×C4 |
| Fitting, socle, cosocle | C2×C53 | C23 |
| prime radical | C2×#92566 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^4,5^3|a^2=d,b^2=d,c^2=d,g^a=g^4,e^b=e^4,f^c=f^4128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 727);