Finite Group DatabasebetaFinite Group Databasebeta| order | 8829 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊#11758281 |
| unambiguous semidirect product | (C3×#11758281)⋊C3 |
| Fitting | C32×C109 ⋊ C9 |
| Sylow | C109 ⋊ C32⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×#11758281 |
| commutator, socle | C3×C109 | C3×C9 |
| Fitting | C32×C109 | C9 |
| hypercenter | C32 | #11758281 |
| hypocenter | C109 | C32⋊C9 |
| LCS | G ▷ C3×C109 ▷ C109 | |
| UCS | C1 ◁ C3 ◁ C32 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,109|a^3=d,b^a=bc,e^a=e^16,e^d=e^63141 conjugacy classes — view the full character table.
| maximal subgroup of | #40996961, #40996962, #40996963, … |
| maximal normal subgroup of | #40996961, #40996962, #40996963, … |
| maximal quotient of | (C3×#11758281)⋊C9, C32⋊#15668885, #40996960, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8829, 52);