Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C33 |
| direct product | C3×C27×C37⋊C3 |
| Fitting | C3×C27×C37 ⋊ C3 |
| derived, Sylow | C37 ⋊ C32×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | C37⋊C3 |
| commutator, hypocenter | C37 | C32×C27 |
| Frattini | C9 | C32×C37⋊C3 |
| Fitting | C3×C27×C37 | C3 |
| socle | C32×C37 | C3×C9 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C27 | |
144 conjugacy classes of subgroups.
1215 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #41004944, #41004946, C9×C27×C37⋊C3, … |
| maximal normal subgroup of | #41004944, #41004946, C9×C27×C37⋊C3, … |
| maximal quotient of | C9×C27×C37⋊C3, C3×C27×#66524, C37⋊C3×C32⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 234);