Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22×C4 |
| direct product | C23×#9719 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | #121 |
| commutator | C42 | C22×C4×C23 |
| Frattini, cosocle | C2×C42 | C23×C23 |
| socle | C22×C23 | #390 |
| prime radical | C23×#3169 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C2×C42×C23 ◁ G | |
506 conjugacy classes of subgroups.
1334 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 2707);