Finite Group DatabasebetaFinite Group Databasebeta| order | 33129 |
| automorphism | ? |
| homology | Abelianization (H1) = C81 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C409⋊C81 |
| derived, Sylow | C409 ⋊ C81 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C27 | C409⋊C3 |
| commutator, hypocenter | C409 | C81 |
| Fitting, cosocle | C27×C409 | C3 |
| socle, prime radical | C3×C409 | C27 |
| LCS | G ▷ C409 | |
| UCS | C1 ◁ C27 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33129 |
Polycyclic presentation:
3^4,409|a^3=b,b^3=c,c^3=d,e^a=e^3553753 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33129, 16);