Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#13133141 |
| Sylow | C53 ⋊ C22×#103 |
816 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 389 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 | #27289661, #27289663, #27290359, … |
| maximal normal subgroup of | #27289661, #27289663, #27290359, … |
| maximal quotient of | C22×Q8⋊#88322, C2×#20273144, C2×#20273118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13000);