Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C25 |
| direct product | C23×#20773 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C23 | C24 |
| commutator | C23 | C23×C4×C23 |
| Frattini, cosocle | C22×C4 | C24×C23 |
| socle | C23×C23 | C23×C4 |
| prime radical | C24×C23 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C23 ◁ G | |
830 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1472 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 13761);