Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C131 ⋊ C2 |
| Sylow | C131 ⋊ #349 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^1301322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #349×D131, C2×#22553093, #30667580, … |
| maximal normal subgroup of | #349×D131, C2×#22553093, #30667580, … |
| maximal quotient of | #30663884, #30663900, #30663918, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 330);