Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C41 · Schur multiplier (H2) = C2×C42 |
| direct product | C4×#97×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C41 | C22 |
| commutator | C2 | C43×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| socle, prime radical | C23×C41 | C22×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C41 ◁ G | |
360 conjugacy classes of subgroups.
3280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7019, C41×#7030, C41×#7149, … |
| maximal normal subgroup of | C41×#7019, C41×#7030, C41×#7149, … |
| maximal quotient of | C4×C41×#322, C8×#97×C41, C41×#7842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 457);