Finite Group DatabasebetaFinite Group Databasebeta| order | 8829 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C109 ⋊ C27⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×#11758281 |
| commutator, socle | C3×C109 | C3×C9 |
| Fitting | C9×C109 | C9 |
| hypercenter | C9 | #11758281 |
| hypocenter | C109 | C27⋊C3 |
| LCS | G ▷ C3×C109 ▷ C109 | |
| UCS | C1 ◁ C3 ◁ C9 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,109|a^3=c,c^3=d,b^a=bd,e^a=e^38,e^b=e^63,e^c=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 | #40996958, #40996960, #40996974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8829, 59);