Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C25 |
| direct product | C4×AGL(1,ℤ/8)×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C2×D4 |
| commutator | C4 | C23×C4×C41 |
| Frattini, cosocle | C2×C4 | C24×C41 |
| socle | C22×C41 | C22×D4 |
| prime radical | C2×AGL(1,ℤ/8)×C41 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G | |
548 conjugacy classes of subgroups.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8954, C41×#8956, C41×#9095, … |
| maximal normal subgroup of | C41×#8954, C41×#8956, C41×#9095, … |
| maximal quotient of | C8×AGL(1,ℤ/8)×C41, C41×#17869, C41×#17871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1676);