Finite Group DatabasebetaFinite Group Databasebeta| order | 27360 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1327104 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C5×C8×C19 |
| multiplicative | (ℤ/35189)ˣ, (ℤ/42501)ˣ, (ℤ/45243)ˣ, (ℤ/47901)ˣ, (ℤ/47943)ˣ, (ℤ/56668)ˣ, (ℤ/63868)ˣ, (ℤ/70378)ˣ, (ℤ/82116)ˣ, (ℤ/85002)ˣ, (ℤ/90486)ˣ, (ℤ/95802)ˣ, (ℤ/95886)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C23×C32×C5×C19 |
| socle, prime radical | C23×C32×C5×C19 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
912 conjugacy classes of subgroups.
27360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.