Finite Group DatabasebetaFinite Group Databasebeta| order | 5328 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 331776 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C37 |
| multiplicative | (ℤ/7805)ˣ, (ℤ/8697)ˣ, (ℤ/9387)ˣ, (ℤ/10035)ˣ, (ℤ/11596)ˣ, (ℤ/15610)ˣ, (ℤ/17394)ˣ, (ℤ/18774)ˣ, (ℤ/20070)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C37 |
| socle, prime radical | C23×C32×C37 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
5328 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.