Finite Group DatabasebetaFinite Group Databasebeta| order | 24864 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 13824 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C7×C16×C37 |
| multiplicative | (ℤ/25199)ˣ, (ℤ/25499)ˣ, (ℤ/29057)ˣ, (ℤ/37299)ˣ, (ℤ/49732)ˣ, (ℤ/50398)ˣ, (ℤ/50998)ˣ, (ℤ/58114)ˣ, (ℤ/74598)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C22×C3×C7×C37 |
| socle, prime radical | C22×C3×C7×C37 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
112 conjugacy classes of subgroups.
24864 conjugacy classes. The character table is too large to display.
| automorphism group of | C113×C223, C43×C593 |
| outer automorphism group of | C113×C223, C43×C593 |
Past the SmallGroups library coverage — no SmallGroups id.