Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #1520 |
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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,b^2=f,c^2=g,d^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,d^b=dg,e^b=efg,h^b=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | #26107815, #26107816, #26107821, … |
| maximal normal subgroup of | #26107815, #26107816, #26107821, … |
| maximal quotient of | #26104277, #26104281, #26104344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 3081);