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 | C27 | C109⋊C3 |
| commutator, hypocenter | C109 | C81 |
| Fitting | C27×C109 | C3 |
| socle | C3×C109 | C27 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C27 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,109|a^3=b,b^3=c,c^3=d,e^a=e^631053 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C81×C109⋊C3, C3×#22579484, #40996768, … |
| maximal normal subgroup of | C81×C109⋊C3, C3×#22579484, #40996768, … |
| maximal quotient of | #40996710, C3×#22579484 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8829, 16);