Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C8×Dic53 |
| derived, Sylow | C53 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D53 |
| commutator, hypocenter | C53 | C22×C4×C8 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C23×C8×C53 | C2 |
| socle | C24×C53 | C2×C4 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23×C8 | |
760 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #336×Dic53, #27289243, #27289247, … |
| maximal normal subgroup of | #336×Dic53, #27289243, #27289247, … |
| maximal quotient of | C22×C8×#88322, C22×#16810345, C2×C8×#11719917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12910);