Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C27 |
| direct product | C2×C41×#380 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C41 | C23 |
| commutator | C22 | C23×C4×C41 |
| Frattini, cosocle | C23 | C24×C41 |
| prime radical | C25×C41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C41 ◁ G | |
1232 conjugacy classes of subgroups.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7915, C2×C41×#1289, C41×#7983, … |
| maximal normal subgroup of | C41×#7915, C2×C41×#1289, C41×#7983, … |
| maximal quotient of | C2×C41×C22⋊#95, C2×C41×#1434, C2×C41×C4⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1010);