Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C34 |
No aliases for this group.
| Sylow | C43 ⋊ 3−1+22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×C43⋊C3 |
| commutator, socle, cosocle | C32×C43 | C34 |
| Fitting | C43×#6891 | C3 |
| prime radical | C34×C43 | C32 |
| hypercenter | #6891 | C43⋊C3 |
| hypocenter | C43 | 3−1+22 |
| LCS | G ▷ C32×C43 ▷ C43 | |
| UCS | C1 ◁ C32 ◁ #6891 | |
836 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 298 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3483 |
Polycyclic presentation:
3^6,43|a^3=f,b^3=e,b^a=be,c^a=cf,g^a=g^6,d^b=de,g^b=g^36835 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 3606);