Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11692 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#11692 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×#99 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C23 |
| prime radical | C23×#2617 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C24×C23 ◁ C22×C22⋊C4×C23 ◁ G | |
670 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 4680);