Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #1393 |
232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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,b^2=e,c^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,h^a=h^46,d^b=dfg,d^c=dg670 conjugacy classes — view the full character table.
| maximal subgroup of | #26103785, #26103786, #26103788, … |
| maximal normal subgroup of | #26103785, #26103786, #26103788, … |
| maximal quotient of | #26103241, #26103279, #26103303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2635);