Finite Group DatabasebetaFinite Group Databasebeta| order | 34083 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C541 ⋊ C9 |
| Sylow | C541 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ #19096457 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #26015499 |
| commutator, hypocenter | C7×C541 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C7×C541 | C3 |
| LCS | G ▷ C7×C541 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34083 |
Polycyclic presentation:
3,7,541,3|a^3=d,b^a=b^4,c^a=c^1293795 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34083, 5);