Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| isoclinism | isoclinic class of Dic94 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C42×C22⋊D47 |
| Fitting | C22×C42×C47 ⋊ C2 |
| Sylow | C47 ⋊ C42×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×D47 |
| commutator | C2×C47 | C22×C42 |
| Frattini | C23 | C23×D47 |
| Fitting | C22×C42×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C22×C42 | D47 |
| hypocenter | C47 | C42×D4 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C42 ◁ C22×C42 | |
924 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 381 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6856);