Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C23 · Schur multiplier (H2) = C26 |
| direct product | C23×#23355 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C23 | C24 |
| commutator | C22 | C23×C8×C23 |
| Frattini, cosocle | C22×C4 | C24×C23 |
| socle | C23×C23 | C23×C4 |
| prime radical | C2×C23×#127 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C23 ◁ G | |
984 conjugacy classes of subgroups; only the 386 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 386 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1748 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 16343);