Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #2093 |
290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 290 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=d,b^2=deg,d^2=g,e^2=g,b^a=bd,c^a=ce,c^b=cf,d^b=dg,e^b=eg,h^b=h^46,d^c=dg,e^c=eg676 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2093, C2×#20244914, #26246071, … |
| maximal normal subgroup of | D47×#2093, C2×#20244914, #26246071, … |
| maximal quotient of | #26121254, #26121293, #26121317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6036);