Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | #322×D47 |
| Fitting | C47×#322 ⋊ C2 |
| Sylow | C47 ⋊ C2×#322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D47 |
| commutator | C2×C47 | C2×C4×C8 |
| Fitting | C47×#322 | C2 |
| socle | C22×C47 | C2×C42 |
| hypercenter | #322 | D47 |
| hypocenter | C47 | C2×#322 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C42 ◁ #322 | |
248 conjugacy classes of subgroups.
1000 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1313, #26125277, #26125329, … |
| maximal normal subgroup of | D47×#1313, #26125277, #26125329, … |
| maximal quotient of | #322×Dic47, D47×#1273, #26106700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2784);