Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C41 · Schur multiplier (H2) = C23 |
| direct product | C2×C41×#366 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C41 | D8 |
| commutator | C8 | C22×C4×C41 |
| Frattini, cosocle | C2×C8 | C23×C41 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C22×C4×C41 ◁ C22×C8×C41 ◁ G | |
168 conjugacy classes of subgroups.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7471, C41×#7478, C4×C41×#366, … |
| maximal normal subgroup of | C41×#7471, C41×#7478, C4×C41×#366, … |
| maximal quotient of | C2×C41×#1371, C41×#12022, C41×#12032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 888);