Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C41 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×M32×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C41 | C22 |
| commutator | C2 | C2×C4×C8×C41 |
| Frattini, cosocle | C2×C8 | C23×C41 |
| socle | C22×C41 | C22×C8 |
| prime radical | C23×C41 | C2×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C41 ◁ G | |
196 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7138, C41×#7139, C41×#7140, … |
| maximal normal subgroup of | C41×#7138, C41×#7139, C41×#7140, … |
| maximal quotient of | C8×M32×C41, C41×#11402, C41×#11409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 839);