Finite Group DatabasebetaFinite Group Databasebeta| order | 4504 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C563⋊C8 |
| derived, Sylow | C563 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D563 |
| commutator, hypocenter | C563 | C8 |
| Fitting, cosocle | C4×C563 | C2 |
| socle, prime radical | C2×C563 | C4 |
| LCS | G ▷ C563 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 571 |
| transitive degree | μt(G) = 4504 |
Polycyclic presentation:
2^3,563|a^2=b,b^2=c,d^a=d^5621132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4504, 6);