Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C25 |
| direct product | C2×C41×#443 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C41 | D4 |
| commutator | C4 | C23×C4×C41 |
| Frattini, cosocle | C2×C4 | C24×C41 |
| socle | C22×C41 | C4×D4 |
| prime radical | C2×#135×C41 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C41 ◁ C22×C8×C41 ◁ G | |
472 conjugacy classes of subgroups.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41×#1335, C41×#11602, C2×C41×#1336, … |
| maximal normal subgroup of | C2×C41×#1335, C41×#11602, C2×C41×#1336, … |
| maximal quotient of | C2×C8×D8×C41, C2×C8×SD16×C41, C2×C8×Q16×C41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1685);