Finite Group DatabasebetaFinite Group Databasebeta| order | 31952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D1997⋊C8 |
| derived, Sylow | C1997 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #22547819 |
| commutator, hypocenter | C1997 | C2×C8 |
| Frattini | C2 | C2×#22547819 |
| Fitting | C4×C1997 | C4 |
| socle | C2×C1997 | C2×C4 |
| prime radical | C2×D1997 | C4 |
| cosocle | Dic1997 | C22 |
| LCS | G ▷ C1997 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15976 |
Polycyclic presentation:
2^4,1997|a^2=c,c^2=d,e^a=e^1585,e^b=e^1996,e^c=e^19962012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31952, 48);