Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C16×C131 ⋊ C2 |
| Sylow | C131 ⋊ #508 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^130,d^b=de,e^b=ef,g^b=g^1302102 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30664144, #30664146, #30664147, … |
| maximal normal subgroup of | #30664144, #30664146, #30664147, … |
| maximal quotient of | #30667669, #30667745, C4×D2096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 981);