Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×D127 |
| Fitting | C2×Q16×C127 ⋊ C2 |
| Sylow | C127 ⋊ C22×Q16 |
258 conjugacy classes of subgroups.
910 conjugacy classes — view the full character table.
| maximal subgroup of | #358×D127, #30640448, #362×D127, … |
| maximal normal subgroup of | #358×D127, #30640448, #362×D127, … |
| maximal quotient of | C2×#103×D127, C2×#107×D127, C4×Q16×D127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1324);