Finite Group DatabasebetaFinite Group Databasebeta| order | 31775 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C31×C41 ⋊ C25 |
| Sylow | C41 ⋊ C31⋊C25 |
| Sylow | C31 ⋊ C41⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #20263757 |
| commutator, hypocenter | C31×C41 | C25 |
| Fitting, socle, prime radical, cosocle | C5×C31×C41 | C5 |
| LCS | G ▷ C31×C41 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31775 |
Polycyclic presentation:
5,31,41,5|a^5=d,b^a=b^4,c^a=c^101295 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31775, 5);