Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C22×#41×C47 ⋊ C2 |
| Sylow | C47 ⋊ #3485 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C22×#41×C47 | C2 |
| hypercenter | C22×#41 | D47 |
| hypocenter | C47 | #3485 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C22×#41 | |
1560 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|c^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^46,d^b=df964 conjugacy classes — view the full character table.
| maximal subgroup of | #26108452, #26108454, #26108873, … |
| maximal normal subgroup of | #26108452, #26108454, #26108873, … |
| maximal quotient of | #26376298, #26376548, #26376573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 18154);