Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C37 ⋊ C81⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C9 | C3×#66526 |
| commutator, socle | C3×C37 | C3×C27 |
| Fitting | C3×C9×C37 | C9 |
| hypercenter | C3×C9 | #66526 |
| hypocenter | C37 | C81⋊C3 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C9 ◁ C3×C9 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|a^3=c,c^3=d,d^3=e,b^a=be,f^a=f^16,f^c=f^26207 conjugacy classes — view the full character table.
| maximal subgroup of | #41008355, #41008356, #41008357, … |
| maximal normal subgroup of | #41008355, #41008356, #41008357, … |
| maximal quotient of | #41008346, C32⋊#15688534, #41008418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 343);