Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#15689064 |
| Sylow | C47 ⋊ C2×#400 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D47 |
| commutator | C23×C47 | C24 |
| Frattini | C23 | C23×D47 |
| Fitting | C2×#95×C47 | C2 |
| socle | C24×C47 | C23 |
| hypercenter | C2×#95 | D47 |
| hypocenter | C47 | C2×#400 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
604 conjugacy classes of subgroups.
964 conjugacy classes — view the full character table.
| maximal subgroup of | #26138122, C4×#15689064, #26141676, … |
| maximal normal subgroup of | #26138122, C4×#15689064, #26141676, … |
| maximal quotient of | C2×#20241639, C2×#20241643, C2×#20241646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7764);