Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #1507 |
346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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=e,c^2=g,d^2=g,b^a=bd,d^a=df,h^a=h^46,c^b=cf,d^b=dg,e^b=efg676 conjugacy classes — view the full character table.
| maximal subgroup of | #26107858, #26107861, #26107863, … |
| maximal normal subgroup of | #26107858, #26107861, #26107863, … |
| maximal quotient of | #26104263, #26104280, #26104310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 3026);