Finite Group DatabasebetaFinite Group Databasebeta| order | 21168 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 870912 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C4×C9×C49 |
| multiplicative | (ℤ/26201)ˣ, (ℤ/30905)ˣ, (ℤ/32585)ˣ, (ℤ/33687)ˣ, (ℤ/34437)ˣ, (ℤ/37233)ˣ, (ℤ/38073)ˣ, (ℤ/39735)ˣ, (ℤ/45916)ˣ, (ℤ/46305)ˣ, (ℤ/50764)ˣ, (ℤ/52402)ˣ, (ℤ/61810)ˣ, (ℤ/65170)ˣ, (ℤ/67374)ˣ, (ℤ/68874)ˣ, (ℤ/74466)ˣ, (ℤ/76146)ˣ, (ℤ/79470)ˣ, (ℤ/92610)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C7 | C23×C32×C7 |
| socle, prime radical | C23×C32×C7 | C2×C3×C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
810 conjugacy classes of subgroups.
21168 conjugacy classes. The character table is too large to display.
| automorphism group of | C5×C19×C343 |
| outer automorphism group of | C5×C19×C343 |
Past the SmallGroups library coverage — no SmallGroups id.