Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #3211 |
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|b^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^46,f^c=fg469 conjugacy classes — view the full character table.
| maximal subgroup of | #26190291, #26190293, #26190302, … |
| maximal normal subgroup of | #26190291, #26190293, #26190302, … |
| maximal quotient of | #26225600, #26225964, #26226805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 15472);