Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #538×D47 |
| Fitting | C47×#538 ⋊ C2 |
| Sylow | C47 ⋊ C2×#538 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C47×#538 | C2 |
| hypercenter | #538 | D47 |
| hypocenter | C47 | C2×#538 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #538 | |
1336 conjugacy classes of subgroups.
550 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1600, D47×#1606, D47×#1612, … |
| maximal normal subgroup of | D47×#1600, D47×#1606, D47×#1612, … |
| maximal quotient of | D47×#2312, D47×#2318, D47×#2321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 17844);