Finite Group DatabasebetaFinite Group Databasebeta| order | 8427 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C4×C13×C53 (order 5512) · Inn(G) = C1 · Out(G) = C2×C4×C13×C53 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C8427 |
| abelian | C3×C2809 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C53 | C3×C53 |
| socle | C3×C53 | C53 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6 conjugacy classes of subgroups.
8427 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8427, 1);