Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C41 · Schur multiplier (H2) = C28 |
| direct product | C41×#3519 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C41 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ G | |
1252 conjugacy classes of subgroups.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8416, C41×#17547, C41×#17597, … |
| maximal normal subgroup of | C41×#8416, C41×#17547, C41×#17597, … |
| maximal quotient of | C41×#34194, C41×#34233, C41×#34236, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2251);