Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C41 · Schur multiplier (H2) = C22 |
| direct product | C41×AGL(1,ℤ/16) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #442 |
| commutator | C8 | C22×C4×C41 |
| Frattini, cosocle | C2×C8 | C23×C41 |
| prime radical | C41×#509 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C2×C4×C41 ◁ #97×C41 ◁ G | |
154 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
943 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C41×AGL(1,ℤ/16), C41×#33468, C41×#33469, … |
| maximal normal subgroup of | C2×C41×AGL(1,ℤ/16), C41×#33468, C41×#33469, … |
| maximal quotient of | C41×#12065, C41×#12067, C41×#12077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 913);