Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C47×#391 ⋊ C2 |
| Sylow | C47 ⋊ #2326 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C47×#391 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | #391 | D47 |
| hypocenter | C47 | #2326 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #391 | |
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^46,c^b=ce,h^b=h^46,h^c=h^46688 conjugacy classes — view the full character table.
| maximal subgroup of | #26125569, #26125767, #26131467, … |
| maximal normal subgroup of | #26125569, #26125767, #26131467, … |
| maximal quotient of | #26137539, #26137585, #26137590, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7224);