Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C131 ⋊ C2 |
| Sylow | C131 ⋊ #481 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|c^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^130,e^c=ef1319 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30664979, #30664980, #30664990, … |
| maximal normal subgroup of | #30664979, #30664980, #30664990, … |
| maximal quotient of | #30666051, #30666154, #30666278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 867);