Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19162 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#19165 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C23 |
| prime radical | C22×D4×C23 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
674 conjugacy classes of subgroups.
989 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 12153);