Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #1831 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D47 |
| commutator | C22×C47 | C22×C8 |
| Fitting | C43×C47 | C2 |
| socle | C23×C47 | C22×C4 |
| hypercenter | C43 | D47 |
| hypocenter | C47 | #1831 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
260 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 149 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=f,b^2=e,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^461528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26102811, #26102812, #26102821, … |
| maximal normal subgroup of | #26102811, #26102812, #26102821, … |
| maximal quotient of | #26109924, #26109928, #26109939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4627);