Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #525×D47 |
| Fitting | C47×#525 ⋊ C2 |
| Sylow | C47 ⋊ C2×#525 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D47 |
| commutator, socle | C22×C47 | C25 |
| Frattini | C22 | C24×D47 |
| Fitting | C47×#525 | C2 |
| hypercenter | #525 | D47 |
| hypocenter | C47 | C2×#525 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
1880 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1501, D47×#1504, #26183438, … |
| maximal normal subgroup of | D47×#1501, D47×#1504, #26183438, … |
| maximal quotient of | D47×#2280, D47×#2290, D47×#2296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 17746);