Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C47×#500 ⋊ C2 |
| Sylow | C47 ⋊ #3169 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#500 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #500 | D47 |
| hypocenter | C47 | #3169 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^46,h^b=h^46,h^d=h^46550 conjugacy classes — view the full character table.
| maximal subgroup of | #26127602, #26127607, #26127622, … |
| maximal normal subgroup of | #26127602, #26127607, #26127622, … |
| maximal quotient of | #26216815, #26220491, #26221459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 15090);