Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×M32×D47 |
| Fitting | C2×M32×C47 ⋊ C2 |
| Sylow | C47 ⋊ C22×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D47 |
| commutator | C2×C47 | C23×C8 |
| Frattini | C8 | C23×D47 |
| Fitting | C2×M32×C47 | C2 |
| socle | C22×C47 | C22×C8 |
| hypercenter | C2×M32 | D47 |
| hypocenter | C47 | C22×M32 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C8 ◁ C2×M32 | |
400 conjugacy classes of subgroups.
1000 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1375, #26131126, D47×#1376, … |
| maximal normal subgroup of | D47×#1375, #26131126, D47×#1376, … |
| maximal quotient of | C2×#346×D47, C4×M32×D47, C2×M32×Dic47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 17604);