Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C131 ⋊ C2 |
| Sylow | C131 ⋊ #418 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^130,c^b=cf,d^b=df,g^b=g^1301322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30665930, #30665932, #30666335, … |
| maximal normal subgroup of | #30665930, #30665932, #30666335, … |
| maximal quotient of | #30664353, #30664379, #30664405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 555);