Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of C5⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C53 |
No aliases for this group.
| derived, Sylow | C53 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | C5⋊(C5⋊D5) |
| commutator, hypocenter | C53 | C16 |
| Fitting, cosocle | C53×C8 | C2 |
| socle, prime radical | C2×C53 | C8 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C8 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2000 |
Polycyclic presentation:
2^4,5^3|a^2=b,b^2=c,c^2=d,e^a=e^4,f^a=f^4,g^a=g^4512 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 470);