Finite Group DatabasebetaFinite Group Databasebeta| order | 31904 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D997⋊C16 |
| derived, Sylow | C997 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #16860614 |
| commutator, hypocenter | C997 | C2×C16 |
| Frattini | C4 | C2×#16860614 |
| Fitting | C8×C997 | C4 |
| socle | C2×C997 | C2×C8 |
| prime radical | C2×D997 | C8 |
| cosocle | #22547562 | C22 |
| LCS | G ▷ C997 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15952 |
Polycyclic presentation:
2^5,997|a^2=c,c^2=d,d^2=e,f^a=f^161,f^b=f^996,f^c=f^9962024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31904, 219);