Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#564 ⋊ C2 |
| Sylow | C47 ⋊ #3567 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C47×#564 | C2 |
| hypercenter | #564 | D47 |
| hypocenter | C47 | #3567 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #564 | |
950 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 449 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=f,d^2=fg,e^2=fg,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^46,c^b=cg,d^b=df,h^b=h^46,h^c=h^46,h^e=h^46475 conjugacy classes — view the full character table.
| maximal subgroup of | #26197961, #26197969, #26197976, … |
| maximal normal subgroup of | #26197961, #26197969, #26197976, … |
| maximal quotient of | #26379618, #26380584, #26380639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 19200);