Finite Group DatabasebetaFinite Group Databasebeta| order | 8829 |
| automorphism | ? |
| homology | Abelianization (H1) = C81 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C109 ⋊ C81 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #15668887 |
| commutator, hypocenter | C109 | C81 |
| Fitting, socle | C3×C109 | C27 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C3 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,109|a^3=b,b^3=c,c^3=d,e^a=e^97,e^b=e^16,e^c=e^6393 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#22579529, #40997010, #40997011, … |
| maximal normal subgroup of | C3×#22579529, #40997010, #40997011, … |
| maximal quotient of | #40997004, C3×#22579529 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8829, 61);