Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C35 |
No aliases for this group.
| Sylow | C37 ⋊ 3−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C33×C37⋊C3 |
| commutator, socle | C3×C37 | C34 |
| Fitting | C3×H(3,𝔽3)×C37 | C3 |
| hypercenter | C3×H(3,𝔽3) | C37⋊C3 |
| hypocenter | C37 | 3−1+4 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C3 ◁ C3×H(3,𝔽3) | |
460 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|a^3=e,b^a=be,d^a=de,f^a=f^26,c^b=ce479 conjugacy classes — view the full character table.
| maximal subgroup of | #41006584, #41006590, #41006593, … |
| maximal normal subgroup of | #41006584, #41006590, #41006593, … |
| maximal quotient of | #41007517, #41007521, #41007523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 308);