Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C41 · Schur multiplier (H2) = C28 |
| direct product | Q8×#41×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C41 |
| socle | C22×C41 | C25 |
| prime radical | C2×#41×C41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ G | |
1068 conjugacy classes of subgroups.
2050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8439, C41×#17509, C41×#17514, … |
| maximal normal subgroup of | C41×#8439, C41×#17509, C41×#17514, … |
| maximal quotient of | C4⋊C4×#41×C41, Q8×#117×C41, C41×#34145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2210);