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) = C27 |
| direct product | C22×C22⋊C8×C41 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C41 | C22 |
| commutator | C2 | C23×C8×C41 |
| Frattini, cosocle | C2×C4 | C24×C41 |
| socle | C24×C41 | C2×C4 |
| prime radical | C25×C41 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C41 ◁ G | |
1072 conjugacy classes of subgroups; only the 520 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 520 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 | C2×C41×#1280, C41×#7907, C41×#7913, … |
| maximal normal subgroup of | C2×C41×#1280, C41×#7907, C41×#7913, … |
| maximal quotient of | C22×C41×#323, C22×C41×#324, C2×C41×#1458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1608);