Finite Group DatabasebetaFinite Group Databasebeta| order | 8829 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C9 |
| direct product | C9×#11758281 |
| Fitting | C9×C109 ⋊ C9 |
| derived, Sylow | C109 ⋊ C92 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #11758281 |
| commutator, hypocenter | C109 | C92 |
| Frattini | C3 | C3×#11758281 |
| Fitting | C9×C109 | C9 |
| socle | C3×C109 | C3×C9 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C9 | |
46 conjugacy classes of subgroups.
189 conjugacy classes — view the full character table.
| maximal subgroup of | C27×#11758281, #40996956, #40996957, … |
| maximal normal subgroup of | C27×#11758281, #40996956, #40996957, … |
| maximal quotient of | (C3×#11758281)⋊C9, C27×#11758281, C9×#15668885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8829, 51);