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×C22⋊Q8×C41 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C41 | C23 |
| commutator, Frattini, cosocle | C22 | C25×C41 |
| prime radical | C25×C41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C41 ◁ G | |
1840 conjugacy classes of subgroups.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8308, C41×#8329, C41×#8550, … |
| maximal normal subgroup of | C41×#8308, C41×#8329, C41×#8550, … |
| maximal quotient of | C22×C41×#380, C22×C41×#385, C22×C41×#387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2165);