Finite Group DatabasebetaFinite Group Databasebeta| order | 31617 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1171 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #24902008 |
| commutator, hypocenter | C1171 | C27 |
| Fitting, socle, prime radical | C3×C1171 | C9 |
| cosocle | #24902006 | C3 |
| LCS | G ▷ C1171 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31617 |
Polycyclic presentation:
3^3,1171|a^3=b,b^3=c,d^a=d^656,d^b=d^420417 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31617, 14);