Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 819147571200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C215 |
| abelian | C25×C4×C41 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2 | C26×C41 |
| socle | C26×C41 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
10552 conjugacy classes of subgroups.
5248 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41×C22⋊#95, C4×C41×#379, C41×#14680, … |
| maximal normal subgroup of | C2×C41×C22⋊#95, C4×C41×#379, C41×#14680, … |
| maximal quotient of | C24×C22⋊C4×C41, C24×C4⋊C4×C41, C23×#117×C41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2319);