Finite Group DatabasebetaFinite Group Databasebeta| order | 4504 |
| automorphism | Aut(G) order 2531248 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1126 |
| unambiguous semidirect product | C563⋊Q8 |
| Sylow | C563 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D563 |
| commutator, socle, prime radical, cosocle | C2×C563 | C22 |
| Fitting | C4×C563 | C2 |
| hypercenter | C4 | D563 |
| hypocenter | C563 | Q8 |
| LCS | G ▷ C2×C563 ▷ C563 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4504 |
Polycyclic presentation:
2^3,563|a^2=c,b^2=c,b^a=bc,d^b=d^5621129 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3378, Dic5630, Dic7882, … |
| maximal quotient of | Dic3378, Dic5630, Dic7882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4504, 11);