Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C47×#335 ⋊ C2 |
| Sylow | C47 ⋊ #1691 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13093999 |
| commutator | C42×C47 | C23 |
| Frattini | C42 | C22×D47 |
| Fitting | C47×#335 | C2 |
| socle | C22×C47 | #121 |
| hypercenter | #335 | D47 |
| hypocenter | C47 | #1691 |
| LCS | G ▷ C42×C47 ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #335 | |
160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 55 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=g,b^2=d,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^46,c^b=cf,e^c=eg,h^c=h^46667 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1691, C2×#20242888, #26198815, … |
| maximal normal subgroup of | D47×#1691, C2×#20242888, #26198815, … |
| maximal quotient of | #26109363, #26112472, #26112486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4010);