Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C24 |
| direct product | C41×#2979 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C24 |
| commutator | C22 | C23×C4×C41 |
| Frattini, cosocle | C2×C4 | C24×C41 |
| socle | C22×C41 | C23×C4 |
| prime radical | C41×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ G | |
410 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 256 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8934, C41×#8935, C41×#9067, … |
| maximal normal subgroup of | C41×#8934, C41×#8935, C41×#9067, … |
| maximal quotient of | C41×#20530, C41×#20538, C41×#20562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1711);