Finite Group DatabasebetaFinite Group Databasebeta| order | 22320 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 138240 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C5×C9×C31 |
| multiplicative | (ℤ/29545)ˣ, (ℤ/34521)ˣ, (ℤ/36861)ˣ, (ℤ/41865)ˣ, (ℤ/41985)ˣ, (ℤ/44648)ˣ, (ℤ/44656)ˣ, (ℤ/46028)ˣ, (ℤ/49148)ˣ, (ℤ/55820)ˣ, (ℤ/59090)ˣ, (ℤ/66972)ˣ, (ℤ/69042)ˣ, (ℤ/73722)ˣ, (ℤ/83730)ˣ, (ℤ/83970)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C3×C5×C31 |
| socle, prime radical | C23×C3×C5×C31 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
22320 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.