Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1828 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C41 · Schur multiplier (H2) = C23 |
| direct product | C41×#1829 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #381 |
| commutator | C23 | C22×C4×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C22×D4×C41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C22×C4×C41 ◁ G | |
272 conjugacy classes of subgroups.
1189 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#12725, C41×#12726, C2×C41×#1829, … |
| maximal normal subgroup of | C41×#12725, C41×#12726, C2×C41×#1829, … |
| maximal quotient of | C41×#8734, C41×#8736, C41×#8751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 561);