Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C47×#322 ⋊ C2 |
| Sylow | C47 ⋊ C8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D47 |
| commutator | C2×C47 | C2×C4×C8 |
| Fitting | C47×#322 | C2 |
| socle | C22×C47 | C2×C42 |
| hypercenter | #322 | D47 |
| hypocenter | C47 | C8×M16 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C42 ◁ #322 | |
224 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 121 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,d^2=f,e^2=g,c^a=cf,h^b=h^46,h^c=h^461000 conjugacy classes — view the full character table.
| maximal subgroup of | C8×M16×D47, C2×#20241667, #26181859, … |
| maximal normal subgroup of | C8×M16×D47, C2×#20241667, #26181859, … |
| maximal quotient of | #26105630, #26105658, #26106702, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2789);