Finite Group DatabasebetaFinite Group Databasebeta| order | 8181 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 388800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C9 |
| abelian | C92×C101 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C32 | C32×C101 |
| socle | C32×C101 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
46 conjugacy classes of subgroups.
8181 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C27×C101, C101×#6864, C101×C9⋊C27, … |
| maximal normal subgroup of | C9×C27×C101, C101×#6864, C101×C9⋊C27, … |
| maximal quotient of | C101×#6855, C9×C27×C101, C101×#6864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8181, 2);