Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C25 |
| direct product | C2×C41×#435 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C41 | C23 |
| commutator | C22 | C23×C4×C41 |
| Frattini, cosocle | C2×C4 | C24×C41 |
| socle | C23×C41 | C22×C4 |
| prime radical | C22×D4×C41 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C41 ◁ G | |
564 conjugacy classes of subgroups.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8161, C41×#8610, C41×#8613, … |
| maximal normal subgroup of | C41×#8161, C41×#8610, C41×#8613, … |
| maximal quotient of | C2×C41×#1581, C2×C41×#1583, C2×C41×#1582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1659);