Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32873 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C22×C42 |
| direct product | C23×#32874 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #2840 |
| commutator, Frattini, cosocle | C24 | C24×C23 |
| prime radical | C22×#41×C23 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C24×C23 ◁ G | |
688 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 25862);