Finite Group DatabasebetaFinite Group Databasebeta| order | 33489 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C61 |
No aliases for this group.
| derived, Sylow | C612 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #26013476 |
| commutator, hypocenter | C612 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C612 | C3 |
| LCS | G ▷ C612 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 549 |
Polycyclic presentation:
3,61^2,3|a^3=d,b^a=b^47,c^a=c^133729 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33489, 8);