Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12741 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C25 |
| direct product | C23×#12743 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #1786 |
| commutator | C2×C8 | C22×C4×C23 |
| Frattini, cosocle | C22×C8 | C23×C23 |
| prime radical | C2×C23×#576 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ C2×C23×#131 ◁ G | |
926 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 5731);