Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | #394×D47 |
| Fitting | C47×#394 ⋊ C2 |
| Sylow | C47 ⋊ C2×#394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C47×#394 | C2 |
| hypercenter | #394 | D47 |
| hypocenter | C47 | C2×#394 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #394 | |
1252 conjugacy classes of subgroups.
550 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1345, #26126958, D47×#1597, … |
| maximal normal subgroup of | D47×#1345, #26126958, D47×#1597, … |
| maximal quotient of | D47×#1438, D47×#1439, D47×#1440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7712);