Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C92 · Schur multiplier (H2) = C32×C9 |
| direct product | C3×C9×#66524 |
| derived, Sylow | C37 ⋊ C3×C92 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C9 | C37⋊C3 |
| commutator, hypocenter | C37 | C3×C92 |
| Frattini | C32 | C32×C37⋊C3 |
| Fitting | C32×C9×C37 | C3 |
| socle | C33×C37 | C32 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C32×C9 | |
252 conjugacy classes of subgroups.
1215 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #41004741, #41004743, #41004789, … |
| maximal normal subgroup of | #41004741, #41004743, #41004789, … |
| maximal quotient of | C92×#66524, C3×#22582441, #41005087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 155);