Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C24 |
| direct product | Q8×M16×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C24 |
| commutator | C22 | C23×C4×C41 |
| Frattini, cosocle | C2×C4 | C24×C41 |
| socle | C22×C41 | C23×C4 |
| prime radical | C23×C41 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ G | |
388 conjugacy classes of subgroups.
2050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8907, C41×#8909, C41×#8990, … |
| maximal normal subgroup of | C41×#8907, C41×#8909, C41×#8990, … |
| maximal quotient of | C4⋊C4×M16×C41, C41×#20520, Q8×#97×C41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1695);