Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C41 · Schur multiplier (H2) = C29 |
| direct product | C22×C4⋊Q8×C41 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C41 | C23 |
| commutator, Frattini, cosocle | C22 | C25×C41 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C41 ◁ G | |
1624 conjugacy classes of subgroups.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8340, C41×#8342, C41×#8551, … |
| maximal normal subgroup of | C41×#8340, C41×#8342, C41×#8551, … |
| maximal quotient of | C22×C41×#384, C22×C41×#389, C22×C41×#391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2173);