Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C47×#432 ⋊ C2 |
| Sylow | C47 ⋊ #1530 |
256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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,e^2=f,b^a=bd,c^a=cf,d^a=df,h^a=h^46,d^b=dg,e^b=efg,h^b=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | #26108161, #26108162, #26108182, … |
| maximal normal subgroup of | #26108161, #26108162, #26108182, … |
| maximal quotient of | #26104291, #26104335, #26104348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 3122);