Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C37 ⋊ #6864 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×#66526 |
| commutator | C3×C37 | C92 |
| Fitting | C3×C9×C37 | C9 |
| socle | C32×C37 | C3×C9 |
| hypercenter | C3×C9 | #66526 |
| hypocenter | C37 | #6864 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C32 ◁ C3×C9 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|a^3=c,b^3=d,c^3=e,b^a=be,f^a=f^16,f^c=f^26207 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#22582688, #41008468, C9×#15688541, … |
| maximal normal subgroup of | C3×#22582688, #41008468, C9×#15688541, … |
| maximal quotient of | #11758603⋊C27, #41008309, #41008355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 316);