Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C131 ⋊ C2 |
| Sylow | C131 ⋊ #510 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^130,d^b=de,e^b=ef,g^b=g^1301316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30667851, #30667854, #30667913, … |
| maximal normal subgroup of | #30667851, #30667854, #30667913, … |
| maximal quotient of | #30667674, #30667682, #30667749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 992);