Finite Group DatabasebetaFinite Group Databasebeta| order | 27264 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 27525120 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C4×C8×C71 |
| multiplicative | (ℤ/59176)ˣ, (ℤ/59745)ˣ, (ℤ/63728)ˣ, (ℤ/79660)ˣ, (ℤ/81888)ˣ, (ℤ/81936)ˣ, (ℤ/88764)ˣ, (ℤ/102420)ˣ, (ℤ/119490)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C24×C3×C71 |
| socle, prime radical | C24×C3×C71 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1520 conjugacy classes of subgroups.
27264 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.