Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C41 · Schur multiplier (H2) = C25 |
| direct product | C41×#1780 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C41 | C23 |
| commutator | C23 | C22×C4×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| socle | C23×C41 | C22×C4 |
| prime radical | C22×#41×C41 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C41 ◁ G | |
612 conjugacy classes of subgroups.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7058, C41×#7305, C41×#7306, … |
| maximal normal subgroup of | C41×#7058, C41×#7305, C41×#7306, … |
| maximal quotient of | C41×#8304, C41×#8305, C41×#8306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 512);