Finite Group DatabasebetaFinite Group Databasebeta| order | 8829 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | 3−1+2×C109 ⋊ C3 |
| Sylow | C109 ⋊ #737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C109⋊C3 |
| commutator, socle | C3×C109 | C33 |
| Fitting | 3−1+2×C109 | C3 |
| hypercenter | 3−1+2 | C109⋊C3 |
| hypocenter | C109 | #737 |
| LCS | G ▷ C3×C109 ▷ C109 | |
| UCS | C1 ◁ C3 ◁ 3−1+2 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,109|c^3=d,b^a=bd,e^a=e^45,e^c=e^63429 conjugacy classes — view the full character table.
| maximal subgroup of | #40996899, #40996902, #40996904, … |
| maximal normal subgroup of | #40996899, #40996902, #40996904, … |
| maximal quotient of | #40996805, #40996807, #40996809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8829, 48);