Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C23 · Schur multiplier (H2) = C2×C4 |
| direct product | C23×#7026 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C23 | C22⋊C4 |
| commutator | C2×C4 | C4×C8×C23 |
| Frattini, cosocle | C22×C42 | C22×C23 |
| socle | C23×C23 | #95 |
| prime radical | C24×C23 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C23 ◁ C22×C42×C23 ◁ G | |
442 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1748 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 14);