Finite Group DatabasebetaFinite Group Databasebeta| order | 27648 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 169869312 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4 |
| abelian | C22×C3×C4×C9×C64 |
| multiplicative | (ℤ/55005)ˣ, (ℤ/57128)ˣ, (ℤ/58672)ˣ, (ℤ/60008)ˣ, (ℤ/60585)ˣ, (ℤ/63232)ˣ, (ℤ/64624)ˣ, (ℤ/66304)ˣ, (ℤ/73340)ˣ, (ℤ/80780)ˣ, (ℤ/83088)ˣ, (ℤ/83376)ˣ, (ℤ/85248)ˣ, (ℤ/85692)ˣ, (ℤ/89856)ˣ, (ℤ/90012)ˣ, (ℤ/103860)ˣ, (ℤ/104220)ˣ, (ℤ/110010)ˣ, (ℤ/121170)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C32 | C24×C32 |
| socle, prime radical | C24×C32 | C2×C3×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
7730 conjugacy classes of subgroups.
27648 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.