Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C41 · Schur multiplier (H2) = C22×C4 |
| direct product | C41×#2769 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C41 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C41 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
344 conjugacy classes of subgroups.
1312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#12147, C41×#12241, C41×#36782, … |
| maximal normal subgroup of | C41×#12147, C41×#12241, C41×#36782, … |
| maximal quotient of | C41×#14387, C41×#14394, C41×#14395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1501);