Finite Group DatabasebetaFinite Group Databasebeta| order | 8829 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C9×C109 ⋊ C9 |
| Sylow | C109 ⋊ C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×#11758281 |
| commutator, socle | C3×C109 | C3×C9 |
| Fitting | C9×C109 | C9 |
| hypercenter | C9 | #11758281 |
| hypocenter | C109 | C9⋊C9 |
| LCS | G ▷ C3×C109 ▷ C109 | |
| UCS | C1 ◁ C3 ◁ C9 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,109|a^3=d,b^3=c,b^a=bc,e^a=e^38,e^d=e^45141 conjugacy classes — view the full character table.
| maximal subgroup of | #40996978, #40996980, #40996982, … |
| maximal normal subgroup of | #40996978, #40996980, #40996982, … |
| maximal quotient of | (C3×#11758281)⋊C9, #40996974, #40996976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8829, 54);