Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C37×C9⋊C9 ⋊ C3 |
| Sylow | C37 ⋊ #6894 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C37⋊C3 |
| commutator, socle | C32×C37 | C33 |
| Fitting | C37×C9⋊C9 | C3 |
| hypercenter | C9⋊C9 | C37⋊C3 |
| hypocenter | C37 | #6894 |
| LCS | G ▷ C32×C37 ▷ C37 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
3^5,37|a^3=e,b^3=d,b^a=bd,c^a=ce,f^b=f^26,f^c=f^10447 conjugacy classes — view the full character table.
| maximal subgroup of | C37⋊C3×#6894, C3×#22582570, #41007576, … |
| maximal normal subgroup of | C37⋊C3×#6894, C3×#22582570, #41007576, … |
| maximal quotient of | #41005101, #41005126, #41005129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 198);