Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×#126×C47 ⋊ C2 |
| Sylow | C47 ⋊ #3560 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C2×#126×C47 | C2 |
| hypercenter | C2×#126 | D47 |
| hypocenter | C47 | #3560 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×#126 | |
1056 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|c^2=f,d^2=fg,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^46,c^b=cg,d^b=df682 conjugacy classes — view the full character table.
| maximal subgroup of | #26108617, #26108621, #26189700, … |
| maximal normal subgroup of | #26108617, #26108621, #26189700, … |
| maximal quotient of | #26379271, #26379379, #26379566, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 19062);