Finite Group DatabasebetaFinite Group Databasebeta| order | 5412 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C52×C8 (order 1600) · Inn(G) = C1 · Out(G) = C23×C52×C8 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C5412 |
| abelian | C3×C4×C11×C41 |
| multiplicative | (ℤ/5413)ˣ, (ℤ/10826)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2 | C2×C3×C11×C41 |
| socle | C2×C3×C11×C41 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24 conjugacy classes of subgroups.
5412 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5412, 1);