Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#7062 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | #99 |
| commutator | C2×C4 | C2×C16×C23 |
| Frattini, cosocle | C2×C4⋊C8 | C22×C23 |
| socle | C22×C23 | #324 |
| prime radical | C23×C23 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C22×C4×C23 ◁ C2×C23×C4⋊C8 ◁ G | |
180 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 50);