Finite Group DatabasebetaFinite Group Databasebeta| order | 11592 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1064448 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C32×C7×C23 |
| multiplicative | (ℤ/14147)ˣ, (ℤ/17931)ˣ, (ℤ/18189)ˣ, (ℤ/20307)ˣ, (ℤ/20433)ˣ, (ℤ/20727)ˣ, (ℤ/23908)ˣ, (ℤ/27076)ˣ, (ℤ/27244)ˣ, (ℤ/28294)ˣ, (ℤ/34812)ˣ, (ℤ/35862)ˣ, (ℤ/36378)ˣ, (ℤ/40614)ˣ, (ℤ/40866)ˣ, (ℤ/41454)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
384 conjugacy classes of subgroups.
11592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C32×C4×C7×C23, C24×C32×C7×C23 |
| maximal normal subgroup of | C22×C32×C4×C7×C23, C24×C32×C7×C23 |
| maximal quotient of | C22×C32×C4×C7×C23, C24×C32×C7×C23 |
Past the SmallGroups library coverage — no SmallGroups id.