Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | #340×D47 |
| Fitting | C47×#340 ⋊ C2 |
| Sylow | C47 ⋊ C2×#340 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D47 |
| commutator | C4×C47 | C2×C42 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#340 | C2 |
| socle | C23×C47 | C2×D4 |
| hypercenter | #340 | D47 |
| hypocenter | C47 | C2×#340 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
512 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 193 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×#1347, D47×#1348, #26126508, … |
| maximal normal subgroup of | D47×#1347, D47×#1348, #26126508, … |
| maximal quotient of | D47×#1277, #26105742, #26105752, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4222);