Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C131 ⋊ #332 |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,b^2=e,c^2=f,d^2=ef,b^a=bc,c^a=ce,c^b=cf,d^b=def,g^b=g^1301319 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #332×D131, C2×#22553057, #30664607, … |
| maximal normal subgroup of | #332×D131, C2×#22553057, #30664607, … |
| maximal quotient of | #30663783, #30663845, #30664012, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 294);