Finite Group DatabasebetaFinite Group Databasebeta| order | 24948 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 116640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C7×C11×C27 |
| multiplicative | (ℤ/25393)ˣ, (ℤ/29113)ˣ, (ℤ/37431)ˣ, (ℤ/37503)ˣ, (ℤ/50786)ˣ, (ℤ/58226)ˣ, (ℤ/74862)ˣ, (ℤ/75006)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C9 | C22×C32×C7×C11 |
| socle, prime radical | C22×C32×C7×C11 | C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
280 conjugacy classes of subgroups.
24948 conjugacy classes. The character table is too large to display.
| automorphism group of | C67×C379 |
| outer automorphism group of | C67×C379 |
Past the SmallGroups library coverage — no SmallGroups id.