Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C41 · Schur multiplier (H2) = C22 |
| direct product | C2×C41×Q64 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C41 | D16 |
| commutator, Frattini, cosocle | C16 | C23×C41 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×C4×C41 ◁ C2×C8×C41 ◁ C2×C16×C41 ◁ G | |
104 conjugacy classes of subgroups.
1558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7538, C41×#7542, C4×C41×Q64, … |
| maximal normal subgroup of | C41×#7538, C41×#7542, C4×C41×Q64, … |
| maximal quotient of | C2×C41×#1416, C2×C41×#1423, C4×C41×Q64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 993);