Finite Group DatabasebetaFinite Group Databasebeta| order | 31936 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #125×C499 ⋊ C2 |
| Sylow | C499 ⋊ #533 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D499 |
| commutator, socle, cosocle | C22×C499 | C24 |
| Fitting | #125×C499 | C2 |
| prime radical | C22×D499 | C23 |
| hypercenter | #125 | D499 |
| hypocenter | C499 | #533 |
| LCS | G ▷ C22×C499 ▷ C499 | |
| UCS | C1 ◁ C22 ◁ #125 | |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15968 |
Polycyclic presentation:
2^6,499|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,g^b=g^498,g^c=g^498,g^d=g^4983514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31936, 1105);