Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #7519 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×#7521 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #1402 |
| commutator | C4⋊Q8 | C2×C4×C23 |
| Frattini, cosocle | #494 | C22×C23 |
| prime radical | C23×#555 | C4 |
| LCS | G ▷ C4⋊Q8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C23 ◁ C2×C4×C23 ◁ C42×C23 ◁ C23×#494 ◁ G | |
148 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 509);