Finite Group DatabasebetaFinite Group Databasebeta| order | 27360 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9289728 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C5×C9×C19 |
| multiplicative | (ℤ/54435)ˣ, (ℤ/56536)ˣ, (ℤ/58064)ˣ, (ℤ/59565)ˣ, (ℤ/63536)ˣ, (ℤ/72200)ˣ, (ℤ/72580)ˣ, (ℤ/79420)ˣ, (ℤ/82512)ˣ, (ℤ/84804)ˣ, (ℤ/103140)ˣ, (ℤ/108300)ˣ, (ℤ/108870)ˣ, (ℤ/119130)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C24×C3×C5×C19 |
| socle, prime radical | C24×C3×C5×C19 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
27360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.