Finite Group DatabasebetaFinite Group Databasebeta| order | 7800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3840 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C13×C25 |
| multiplicative | (ℤ/7979)ˣ, (ℤ/8003)ˣ, (ℤ/9107)ˣ, (ℤ/9755)ˣ, (ℤ/9875)ˣ, (ℤ/11709)ˣ, (ℤ/15958)ˣ, (ℤ/16006)ˣ, (ℤ/18214)ˣ, (ℤ/19510)ˣ, (ℤ/19750)ˣ, (ℤ/23418)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5 | C22×C3×C5×C13 |
| socle, prime radical | C22×C3×C5×C13 | C2×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
96 conjugacy classes of subgroups.
7800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.