Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C41 · Schur multiplier (H2) = C210 |
| direct product | C22×C4×D4×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C41 | C22 |
| commutator | C2 | C24×C4×C41 |
| Frattini, cosocle | C22 | C25×C41 |
| socle | C24×C41 | C23 |
| prime radical | C23×D4×C41 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C41 ◁ G | |
2528 conjugacy classes of subgroups.
3280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8301, C41×#8302, C41×#8310, … |
| maximal normal subgroup of | C41×#8301, C41×#8302, C41×#8310, … |
| maximal quotient of | C22×C4×C22⋊C4×C41, C22×C4×C4⋊C4×C41, C2×C42×D4×C41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2154);