Finite Group DatabasebetaFinite Group Databasebeta| order | 24624 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 559872 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C4 |
| abelian | C3×C42×C19×C27 |
| multiplicative | (ℤ/24961)ˣ, (ℤ/26689)ˣ, (ℤ/49922)ˣ, (ℤ/53378)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C9 | C22×C32×C19 |
| socle, prime radical | C22×C32×C19 | C22×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
420 conjugacy classes of subgroups.
24624 conjugacy classes. The character table is too large to display.
| automorphism group of | C109×C229 |
| outer automorphism group of | C109×C229 |
Past the SmallGroups library coverage — no SmallGroups id.