Finite Group DatabasebetaFinite Group Databasebeta| order | 33282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C43⋊C3)⋊D43) |
| unambiguous semidirect product | (C43⋊C3)⋊D129 |
| Fitting, socle, derived | C3×C432 ⋊ C2×C3 |
| Hall | C3×C43×C43⋊C3 ⋊ C2 |
| Sylow | C432 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C432 | C2×C3 |
| LCS | G ▷ C3×C432 | |
| UCS | C1 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 387 |
Polycyclic presentation:
2,3^2,43^2|c^a=c^2,d^a=d^42,e^a=e^42,d^b=d^361101 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33282, 50);