Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
| direct product | C2×#15688900 |
| Sylow | C47 ⋊ C2×#347 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic47 |
| commutator | C4×C47 | C2×C42 |
| Frattini | C2×C8 | C22×D47 |
| Fitting | C2×M32×C47 | C2 |
| socle | C22×C47 | #97 |
| hypercenter | C2×M32 | D47 |
| hypocenter | C47 | C2×#347 |
| LCS | G ▷ C4×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M32 | |
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
964 conjugacy classes — view the full character table.
| maximal subgroup of | #347×Dic47, C4×#15688900, #26131107, … |
| maximal normal subgroup of | #347×Dic47, C4×#15688900, #26131107, … |
| maximal quotient of | C2×#20241308, C2×#20241310, #26125278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6111);