Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #1378 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | (C2×D47)⋊C4 |
| commutator | C22×C47 | C4×C8 |
| Frattini | C22×C8 | C2×D47 |
| Fitting | C47×#405 | C2 |
| socle | C2×C47 | #336 |
| hypercenter | #405 | D47 |
| hypocenter | C47 | #1378 |
| LCS | G ▷ C22×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C8 ◁ C22×C8 ◁ #405 | |
132 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 77 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=d,b^2=e,d^2=f,f^2=g,b^a=bc,e^a=eg,h^a=h^46,c^b=cg964 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1378, C2×#20241474, #26131301, … |
| maximal normal subgroup of | D47×#1378, C2×#20241474, #26131301, … |
| maximal quotient of | #26103114, #26103124, #26103131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2596);