Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #1916 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D47 |
| commutator | C22×C47 | C22×C8 |
| Fitting | C4×C4⋊C4×C47 | C2 |
| socle | C23×C47 | C22×C4 |
| hypercenter | C4×C4⋊C4 | D47 |
| hypocenter | C47 | #1916 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^46,h^b=h^46976 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1916, C2×#20243947, #26218332, … |
| maximal normal subgroup of | D47×#1916, C2×#20243947, #26218332, … |
| maximal quotient of | #26114397, #26114404, #26114411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 5069);