Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C41 · Schur multiplier (H2) = C22 |
| direct product | C41×#2258 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C41 | C22 |
| commutator | C2 | C22×C16×C41 |
| Frattini, cosocle | C16 | C23×C41 |
| socle | C2×C41 | C22×C16 |
| prime radical | #41×C41 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C32×C41 ◁ G | |
106 conjugacy classes of subgroups.
3280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7514, C41×#13647, C41×#13648, … |
| maximal normal subgroup of | C41×#7514, C41×#13647, C41×#13648, … |
| maximal quotient of | C41×#13549, C41×#13554, C41×#13628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 990);