Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C41 · Schur multiplier (H2) = C25 |
| direct product | C8×#41×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C41 | C22 |
| commutator | C2 | C23×C8×C41 |
| Frattini, cosocle | C2×C4 | C24×C41 |
| socle | C22×C41 | C23×C4 |
| prime radical | C2×#41×C41 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C41 ◁ G | |
456 conjugacy classes of subgroups.
3280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#104×C41, C41×#8191, C41×#8192, … |
| maximal normal subgroup of | C8×#104×C41, C41×#8191, C41×#8192, … |
| maximal quotient of | C8×#117×C41, C4×C8×D4×C41, C4×C8×Q8×C41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1696);