Finite Group DatabasebetaFinite Group Databasebeta| order | 8397 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 33480 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3 |
| abelian | C3×C9×C311 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C3 | C32×C311 |
| socle | C32×C311 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
20 conjugacy classes of subgroups.
8397 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C92×C311, C32⋊C9×C311, C9⋊C9×C311, … |
| maximal normal subgroup of | C92×C311, C32⋊C9×C311, C9⋊C9×C311, … |
| maximal quotient of | C92×C311, C32⋊C9×C311, C9⋊C9×C311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8397, 2);