Finite Group DatabasebetaFinite Group Databasebeta| order | 26880 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 301989888 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C43 |
| abelian | C2×C3×C42×C5×C7×C8 |
| multiplicative | (ℤ/41615)ˣ, (ℤ/46371)ˣ, (ℤ/53505)ˣ, (ℤ/54795)ˣ, (ℤ/56608)ˣ, (ℤ/58448)ˣ, (ℤ/61828)ˣ, (ℤ/67360)ˣ, (ℤ/73060)ˣ, (ℤ/83230)ˣ, (ℤ/92742)ˣ, (ℤ/107010)ˣ, (ℤ/109590)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C4 | C24×C3×C5×C7 |
| socle, prime radical | C24×C3×C5×C7 | C22×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8184 conjugacy classes of subgroups.
26880 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.