Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8×C19 · Schur multiplier (H2) = C29 |
| direct product | C19×#60276 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C19 | C24 |
| commutator | C2 | C24×C8×C19 |
| Frattini, cosocle | C2×C4 | C25×C19 |
| socle | C22×C19 | C24×C4 |
| prime radical | C22×#41×C19 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C19 ◁ G | |
2306 conjugacy classes of subgroups.
2584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 53264);