Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | #334×D47 |
| Fitting | C47×#334 ⋊ C2 |
| Sylow | C47 ⋊ C2×#334 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D47 |
| commutator | C4×C47 | C22×C8 |
| Frattini | C42 | C22×D47 |
| Fitting | C47×#334 | C2 |
| socle | C22×C47 | C2×C4⋊C4 |
| hypercenter | #334 | D47 |
| hypocenter | C47 | C2×#334 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ #334 | |
200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
700 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1333, D47×#1334, #26126046, … |
| maximal normal subgroup of | D47×#1333, D47×#1334, #26126046, … |
| maximal quotient of | D47×#1277, #26107458, #334×Dic47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 3249);