Finite Group DatabasebetaFinite Group Databasebeta| order | 24336 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1437696 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C169 |
| multiplicative | (ℤ/42609)ˣ, (ℤ/42651)ˣ, (ℤ/46137)ˣ, (ℤ/56812)ˣ, (ℤ/61516)ˣ, (ℤ/73044)ˣ, (ℤ/79092)ˣ, (ℤ/85218)ˣ, (ℤ/85302)ˣ, (ℤ/92274)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C13 | C23×C32×C13 |
| socle, prime radical | C23×C32×C13 | C2×C13 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
486 conjugacy classes of subgroups.
24336 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.