Finite Group DatabasebetaFinite Group Databasebeta| order | 28152 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2838528 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C32×C17×C23 |
| multiplicative | (ℤ/33887)ˣ, (ℤ/42951)ˣ, (ℤ/43569)ˣ, (ℤ/49287)ˣ, (ℤ/57268)ˣ, (ℤ/65716)ˣ, (ℤ/67774)ˣ, (ℤ/84492)ˣ, (ℤ/85902)ˣ, (ℤ/87138)ˣ, (ℤ/98574)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
384 conjugacy classes of subgroups.
28152 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.