Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C41 · Schur multiplier (H2) = C2 |
| direct product | C41×#1417 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | D16 |
| commutator | C16 | C2×C4×C41 |
| Frattini, cosocle | C2×C16 | C22×C41 |
| socle | C2×C41 | #357 |
| prime radical | C41×#508 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C2×C4×C41 ◁ C2×C8×C41 ◁ C2×C16×C41 ◁ G | |
72 conjugacy classes of subgroups.
1558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41×#1417, C41×#13620, C41×#13655, … |
| maximal normal subgroup of | C2×C41×#1417, C41×#13620, C41×#13655, … |
| maximal quotient of | C41×#7383, C41×#7384, C41×#7420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 149);