Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C41 · Schur multiplier (H2) = C29 |
| direct product | C41×#3585 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | C23×D4 |
| commutator, Frattini, cosocle | C4 | C25×C41 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C2×#41×C41 ◁ G | |
1464 conjugacy classes of subgroups.
1681 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#23872, C41×#23874, C41×#23882, … |
| maximal normal subgroup of | C41×#23872, C41×#23874, C41×#23882, … |
| maximal quotient of | C41×#60087, C41×#60089, C41×#60109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2317);