Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #1278 |
172 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 172 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=d,b^2=e,c^2=f,d^2=g,e^2=g,b^a=bc,c^a=cf,e^a=ef,h^a=h^461528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×#1278, C2×#20241225, #26105772, … |
| maximal normal subgroup of | D47×#1278, C2×#20241225, #26105772, … |
| maximal quotient of | #26102806, #26102818, #26102824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2347);