Finite Group DatabasebetaFinite Group Databasebeta| order | 8829 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C109 ⋊ C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×C109⋊C3 |
| commutator | C3×C109 | C3×C9 |
| Fitting | C3×C9×C109 | C3 |
| socle | C32×C109 | C32 |
| hypercenter | C3×C9 | C109⋊C3 |
| hypocenter | C109 | C9⋊C9 |
| LCS | G ▷ C3×C109 ▷ C109 | |
| UCS | C1 ◁ C32 ◁ C3×C9 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,109|a^3=d,b^3=c,b^a=bc,e^b=e^631005 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊C9×C109⋊C3, C3×#22579488, #40996805, … |
| maximal normal subgroup of | C9⋊C9×C109⋊C3, C3×#22579488, #40996805, … |
| maximal quotient of | #40996711, #40996758, #40996761, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8829, 20);