Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C23 · Schur multiplier (H2) = C29 |
| direct product | C23×C23×SD32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C23 | D8 |
| commutator, Frattini, cosocle | C8 | C25×C23 |
| prime radical | C23×D8×C23 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C23 ◁ C23×C4×C23 ◁ C23×C8×C23 ◁ G | |
2334 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.
This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 1054 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 55614);