Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #443×D47 |
| Fitting | C47×#443 ⋊ C2 |
| Sylow | C47 ⋊ C2×#443 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D47 |
| commutator | C4×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#443 | C2 |
| socle | C2×C47 | C2×C4×D4 |
| hypercenter | #443 | D47 |
| hypocenter | C47 | C2×#443 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #443 | |
472 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1335, #26126063, D47×#1336, … |
| maximal normal subgroup of | D47×#1335, #26126063, D47×#1336, … |
| maximal quotient of | C8×D8×D47, C8×SD16×D47, C8×Q16×D47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13396);