Finite Group DatabasebetaFinite Group Databasebeta| order | 7128 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 311040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C9 |
| abelian | C2×C4×C92×C11 |
| multiplicative | (ℤ/7363)ˣ, (ℤ/7543)ˣ, (ℤ/10719)ˣ, (ℤ/14726)ˣ, (ℤ/15086)ˣ, (ℤ/21438)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C22×C32×C11 |
| socle, prime radical | C22×C32×C11 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
368 conjugacy classes of subgroups.
7128 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.