Finite Group DatabasebetaFinite Group Databasebeta| order | 31568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D1973⋊C8 |
| derived, Sylow | C1973 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #21463563 |
| commutator, hypocenter | C1973 | C2×C8 |
| Frattini | C2 | C2×#21463563 |
| Fitting | C4×C1973 | C4 |
| socle | C2×C1973 | C2×C4 |
| prime radical | C2×D1973 | C4 |
| cosocle | Dic1973 | C22 |
| LCS | G ▷ C1973 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15784 |
Polycyclic presentation:
2^4,1973|a^2=c,c^2=d,e^a=e^259,e^b=e^1972,e^c=e^19721988 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31568, 48);