Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C131 ⋊ C2 |
| Sylow | C131 ⋊ #361 |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^130,c^b=cef,d^b=df,e^b=ef,g^b=g^1301316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #361×D131, C2×#22553126, #30667709, … |
| maximal normal subgroup of | #361×D131, C2×#22553126, #30667709, … |
| maximal quotient of | #30663929, #30663977, #30664008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 363);