Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C41 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×#127×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C41 | C23 |
| commutator | C22 | C23×C4×C41 |
| Frattini, cosocle | C23 | C24×C41 |
| socle | C23×C41 | C24 |
| prime radical | C2×#127×C41 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C41 ◁ G | |
924 conjugacy classes of subgroups; only the 368 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 368 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7569, C41×#7587, C41×#7603, … |
| maximal normal subgroup of | C41×#7569, C41×#7587, C41×#7603, … |
| maximal quotient of | C4×C41×#390, C4×C41×#384, C4×C41×#392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1038);