Finite Group DatabasebetaFinite Group Databasebeta| order | 8019 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1473863040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C36 |
| abelian | C33×C11×C27 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C9 | C34×C11 |
| socle | C34×C11 | C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1160 conjugacy classes of subgroups.
8019 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C33×C11×C27, C33×C11×C81, C34×C11×C27, … |
| maximal normal subgroup of | C2×C33×C11×C27, C33×C11×C81, C34×C11×C27, … |
| maximal quotient of | C2×C33×C11×C27, C33×C11×C81, C34×C11×C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8019, 475);