Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C41 · Schur multiplier (H2) = C25 |
| direct product | C2×C8×Q8×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C41 | C22 |
| commutator | C2 | C23×C8×C41 |
| Frattini, cosocle | C2×C4 | C24×C41 |
| socle, prime radical | C23×C41 | C22×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C41 ◁ G | |
440 conjugacy classes of subgroups; only the 392 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 392 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 | C8×#101×C41, C41×#8165, C8×#103×C41, … |
| maximal normal subgroup of | C8×#101×C41, C41×#8165, C8×#103×C41, … |
| maximal quotient of | C2×C8×C4⋊C4×C41, C4×C8×Q8×C41, C2×C41×#1916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1690);