Finite Group DatabasebetaFinite Group Databasebeta| order | 19488 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7225344 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C7×C29 |
| multiplicative | (ℤ/35931)ˣ, (ℤ/38055)ˣ, (ℤ/40592)ˣ, (ℤ/43365)ˣ, (ℤ/46256)ˣ, (ℤ/47096)ˣ, (ℤ/47908)ˣ, (ℤ/50740)ˣ, (ℤ/57820)ˣ, (ℤ/58488)ˣ, (ℤ/60552)ˣ, (ℤ/61596)ˣ, (ℤ/70644)ˣ, (ℤ/71862)ˣ, (ℤ/76110)ˣ, (ℤ/86730)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C7×C29 |
| socle, prime radical | C24×C3×C7×C29 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
944 conjugacy classes of subgroups.
19488 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.