Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×Dic131 |
| Sylow | C131 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
938 conjugacy classes — view the full character table.
| maximal subgroup of | #30667810, SD32×Dic131, #30667817, … |
| maximal normal subgroup of | #30667810, SD32×Dic131, #30667817, … |
| maximal quotient of | Q16×C131⋊C8, #30664812, #30664858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 644);