Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#62013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C19 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#529 ◁ G | |
1790 conjugacy classes of subgroups.
931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 55001);