Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C22 |
| direct product | C53×#1618 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C53 |
| prime radical | C53×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1219 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C53×#1618, C53×#18121, C53×#18127, … |
| maximal normal subgroup of | C2×C53×#1618, C53×#18121, C53×#18127, … |
| maximal quotient of | C53×#7790, C53×#7793, C53×#7796, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 350);