Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 248832 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C4×C9×C13 |
| multiplicative | (ℤ/7049)ˣ, (ℤ/7505)ˣ, (ℤ/8769)ˣ, (ℤ/8949)ˣ, (ℤ/9063)ˣ, (ℤ/9633)ˣ, (ℤ/10017)ˣ, (ℤ/10665)ˣ, (ℤ/11692)ˣ, (ℤ/11932)ˣ, (ℤ/12844)ˣ, (ℤ/14098)ˣ, (ℤ/15010)ˣ, (ℤ/16956)ˣ, (ℤ/17538)ˣ, (ℤ/17898)ˣ, (ℤ/18126)ˣ, (ℤ/18252)ˣ, (ℤ/19266)ˣ, (ℤ/20034)ˣ, (ℤ/21330)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C32×C13 |
| socle, prime radical | C23×C32×C13 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
540 conjugacy classes of subgroups.
5616 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.