Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #563×D47 |
| Fitting | C47×#563 ⋊ C2 |
| Sylow | C47 ⋊ C2×#563 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C47×#563 | C2 |
| hypercenter | #563 | D47 |
| hypocenter | C47 | C2×#563 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #563 | |
1024 conjugacy classes of subgroups.
475 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1657, D47×#1660, D47×#1664, … |
| maximal normal subgroup of | D47×#1657, D47×#1660, D47×#1664, … |
| maximal quotient of | D47×#2376, D47×#2378, D47×#2379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 18638);