Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#15688879 |
| Sylow | C47 ⋊ C2×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic47 |
| commutator | C4×C47 | C2×C42 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C2×#117×C47 | C2 |
| socle | C22×C47 | #95 |
| hypercenter | C2×#117 | D47 |
| hypocenter | C47 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#117 | |
404 conjugacy classes of subgroups.
964 conjugacy classes — view the full character table.
| maximal subgroup of | H(3,ℤ/4)×Dic47, C4×#15688879, #26121446, … |
| maximal normal subgroup of | H(3,ℤ/4)×Dic47, C4×#15688879, #26121446, … |
| maximal quotient of | C2×#20241216, C2×#20241217, #26105676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4210);