Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C47 ⋊ C2 |
| Sylow | C47 ⋊ #3499 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C2×C4⋊Q8×C47 | C2 |
| hypercenter | C2×C4⋊Q8 | D47 |
| hypocenter | C47 | #3499 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊Q8 | |
1476 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=f,c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^46688 conjugacy classes — view the full character table.
| maximal subgroup of | #26108194, #26108198, #26108505, … |
| maximal normal subgroup of | #26108194, #26108198, #26108505, … |
| maximal quotient of | #26376380, #26376647, #26376651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 18293);