Finite Group DatabasebetaFinite Group Databasebeta| order | 19376 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 198144 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C7×C173 |
| multiplicative | (ℤ/30189)ˣ, (ℤ/36345)ˣ, (ℤ/38768)ˣ, (ℤ/40252)ˣ, (ℤ/48460)ˣ, (ℤ/60378)ˣ, (ℤ/72690)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C7×C173 |
| socle, prime radical | C23×C7×C173 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
108 conjugacy classes of subgroups.
19376 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.