Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D47 |
| commutator, socle | C2×C47 | C22×C16 |
| Fitting | C47×#504 | C2 |
| hypercenter | #504 | D47 |
| hypocenter | C47 | #2258 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C16 ◁ #504 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^46,c^b=cg1000 conjugacy classes — view the full character table.
| maximal subgroup of | #26136839, #26136842, #26136844, … |
| maximal normal subgroup of | #26136839, #26136842, #26136844, … |
| maximal quotient of | #26136458, #26136475, #26136764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6804);