Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| direct product | #390×D47 |
| Fitting | C47×#390 ⋊ C2 |
| Sylow | C47 ⋊ C2×#390 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C47×#390 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | #390 | D47 |
| hypocenter | C47 | C2×#390 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #390 | |
1360 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1270, #26104261, #26104353, … |
| maximal normal subgroup of | D47×#1270, #26104261, #26104353, … |
| maximal quotient of | D47×C4⋊#95, D47×#1437, #26137461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6963);