Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#14523238 |
| Sylow | C127 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
1288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30637534, C8×#14523238, #30637546, … |
| maximal normal subgroup of | #30637534, C8×#14523238, #30637546, … |
| maximal quotient of | C8×#14523238, #30637578, #30637580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 642);