Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C41 · Schur multiplier (H2) = C2×C42 |
| direct product | C41×#2811 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C41 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C41 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
432 conjugacy classes of subgroups.
1312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7749, C41×#7759, C41×#7812, … |
| maximal normal subgroup of | C41×#7749, C41×#7759, C41×#7812, … |
| maximal quotient of | C41×#14467, C41×#14601, C41×#15510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1543);