Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 220200960 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C43 |
| abelian | C2×C43×C41 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C23 | C24×C41 |
| socle | C24×C41 | C23 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1272 conjugacy classes of subgroups.
5248 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41×#1276, C41×#7867, C4×C41×#336, … |
| maximal normal subgroup of | C2×C41×#1276, C41×#7867, C4×C41×#336, … |
| maximal quotient of | C2×C4×#95×C41, C4×C41×#376, C42×C22⋊C4×C41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 997);