Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C41 · Schur multiplier (H2) = C24×C42 |
| direct product | C2×C41×#376 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C41 | C22 |
| commutator | C2 | C22×C42×C41 |
| Frattini, cosocle | C23 | C24×C41 |
| socle, prime radical | C24×C41 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C41 ◁ G | |
840 conjugacy classes of subgroups.
3280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41×#1274, C41×#7855, C41×#7906, … |
| maximal normal subgroup of | C2×C41×#1274, C41×#7855, C41×#7906, … |
| maximal quotient of | C2×C4×#95×C41, C4×C41×#376, C2×C41×#1434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 999);