Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23×C32 · Schur multiplier (H2) = C2 |
| direct product | C23×Q8⋊C32 |
| unambiguous semidirect product | Q8⋊(C23×C32) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C23 | D4 |
| commutator | C4 | C2×C23×C32 |
| Frattini, cosocle | C4×C16 | C22×C23 |
| socle, prime radical | C22×C23 | C22⋊C16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C23 ◁ C4×C16×C23 ◁ G | |
118 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 380);