Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C41 · Schur multiplier (H2) = C2 |
| direct product | C41×#2104 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #401 |
| commutator, Frattini, cosocle | C24 | C23×C41 |
| prime radical | C24×C41 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C24×C41 ◁ G | |
178 conjugacy classes of subgroups.
943 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C41×#2104, C41×#23847, C41×#32700, … |
| maximal normal subgroup of | C2×C41×#2104, C41×#23847, C41×#32700, … |
| maximal quotient of | C41×#10690, C41×#10691, C41×#11318, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 836);