Finite Group DatabasebetaFinite Group Databasebeta| order | 8667 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 34344 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3 |
| abelian | C3×C27×C107 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C9 | C32×C107 |
| socle | C32×C107 | C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
28 conjugacy classes of subgroups.
8667 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C27×C107, C107×#6864, C107×C32⋊C27, … |
| maximal normal subgroup of | C9×C27×C107, C107×#6864, C107×C32⋊C27, … |
| maximal quotient of | C9×C27×C107, C107×C32⋊C27, C107×C9⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8667, 5);