Finite Group DatabasebetaFinite Group Databasebeta| order | 25776 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 205056 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C9×C179 |
| multiplicative | (ℤ/34105)ˣ, (ℤ/39849)ˣ, (ℤ/48465)ˣ, (ℤ/53132)ˣ, (ℤ/68210)ˣ, (ℤ/79698)ˣ, (ℤ/96930)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C3×C179 |
| socle, prime radical | C23×C3×C179 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
162 conjugacy classes of subgroups.
25776 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.