Finite Group DatabasebetaFinite Group Databasebeta| order | 5008 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C3×C4×C8×C13 (order 2496) · Inn(G) = C1 · Out(G) = C2×C3×C4×C8×C13 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C5008 |
| abelian | C16×C313 |
| multiplicative | (ℤ/5009)ˣ, (ℤ/10018)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C8 | C2×C313 |
| socle | C2×C313 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
10 conjugacy classes of subgroups.
5008 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5008, 1);