Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C41 · Schur multiplier (H2) = C25 |
| direct product | C22×SD32×C41 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | D8 |
| commutator, Frattini, cosocle | C8 | C24×C41 |
| prime radical | C22×D8×C41 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C22×C4×C41 ◁ C22×C8×C41 ◁ G | |
400 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#13013, C41×#13014, C41×#13018, … |
| maximal normal subgroup of | C41×#13013, C41×#13014, C41×#13018, … |
| maximal quotient of | C22×C41×#357, C22×C41×#358, C22×C41×#367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2141);