Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C25 |
| direct product | C4×C4⋊Q8×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C41 | C23 |
| commutator | C22 | C23×C4×C41 |
| Frattini, cosocle | C23 | C24×C41 |
| socle, prime radical | C23×C41 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C41 ◁ G | |
588 conjugacy classes of subgroups.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7570, C41×#7571, C41×#7588, … |
| maximal normal subgroup of | C41×#7570, C41×#7571, C41×#7588, … |
| maximal quotient of | C4×C41×#389, C4×C41×#391, C4×C41×#384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1039);