Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×2−1+4×C47 ⋊ C2 |
| Sylow | C47 ⋊ #3487 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C2×2−1+4×C47 | C2 |
| hypercenter | C2×2−1+4 | D47 |
| hypocenter | C47 | #3487 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|b^2=f,c^2=f,d^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^46826 conjugacy classes — view the full character table.
| maximal subgroup of | #26131838, #26225456, #26247706, … |
| maximal normal subgroup of | #26131838, #26225456, #26247706, … |
| maximal quotient of | #26376306, #26376568, #26377213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 18165);