Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4423680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3×C5 |
| abelian | C22×C32×C4×C52 |
| multiplicative | (ℤ/4433)ˣ, (ℤ/4697)ˣ, (ℤ/5425)ˣ, (ℤ/5673)ˣ, (ℤ/6039)ˣ, (ℤ/6975)ˣ, (ℤ/7564)ˣ, (ℤ/8866)ˣ, (ℤ/9394)ˣ, (ℤ/10850)ˣ, (ℤ/11346)ˣ, (ℤ/12078)ˣ, (ℤ/13950)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C52 |
| socle, prime radical | C23×C32×C52 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1296 conjugacy classes of subgroups.
3600 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.