Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #1270 |
202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=d,c^2=f,d^2=g,b^a=bc,c^a=ce,h^a=h^46,c^b=cf,d^b=def682 conjugacy classes — view the full character table.
| maximal subgroup of | #26103636, #26103637, #26103703, … |
| maximal normal subgroup of | #26103636, #26103637, #26103703, … |
| maximal quotient of | #26102829, #26103022, #26103024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2331);