Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C34 |
| direct product | C9×C32⋊(C37⋊C3) |
| Fitting | C32×C9×C37 ⋊ C3 |
| Sylow | C37 ⋊ C9×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | C3×C37⋊C3 |
| commutator | C3×C37 | C32×C9 |
| Frattini | C32 | C32×C37⋊C3 |
| Fitting | C32×C9×C37 | C3 |
| socle | C32×C37 | C33 |
| hypercenter | C32×C9 | C37⋊C3 |
| hypocenter | C37 | C9×H(3,𝔽3) |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C3×C9 ◁ C32×C9 | |
202 conjugacy classes of subgroups.
1071 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #41004745, #41004747, #41004762, … |
| maximal normal subgroup of | #41004745, #41004747, #41004762, … |
| maximal quotient of | C9×C32⋊#66524, C9×#15688502, #41005122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 168);