Finite Group DatabasebetaFinite Group Databasebeta| order | 28392 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14976 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C7×C169 |
| multiplicative | (ℤ/29111)ˣ, (ℤ/33131)ˣ, (ℤ/33173)ˣ, (ℤ/42591)ˣ, (ℤ/42597)ˣ, (ℤ/56788)ˣ, (ℤ/58222)ˣ, (ℤ/66262)ˣ, (ℤ/66346)ˣ, (ℤ/85182)ˣ, (ℤ/85194)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C13 | C22×C3×C7×C13 |
| socle, prime radical | C22×C3×C7×C13 | C2×C13 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
96 conjugacy classes of subgroups.
28392 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.