Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6720 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C3×C25×C29 |
| multiplicative | (ℤ/8909)ˣ, (ℤ/10157)ˣ, (ℤ/13059)ˣ, (ℤ/17818)ˣ, (ℤ/20314)ˣ, (ℤ/26118)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C5 | C22×C3×C5×C29 |
| socle | C22×C3×C5×C29 | C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
60 conjugacy classes of subgroups.
8700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 9);