Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#13133137 |
| Fitting | C22×C4⋊C4×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×#102 |
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289655, #27289657, #27290353, … |
| maximal normal subgroup of | #27289655, #27289657, #27290353, … |
| maximal quotient of | C22×#16810350, C2×#20273139, C2×#20273113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12995);