Finite Group DatabasebetaFinite Group Databasebeta| order | 11592 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 133056 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C7×C9×C23 |
| multiplicative | (ℤ/17907)ˣ, (ℤ/23876)ˣ, (ℤ/35814)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C3×C7×C23 |
| socle, prime radical | C23×C3×C7×C23 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
11592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C4×C7×C9×C23, C24×C7×C9×C23 |
| maximal normal subgroup of | C22×C4×C7×C9×C23, C24×C7×C9×C23 |
| maximal quotient of | C22×C4×C7×C9×C23, C24×C7×C9×C23 |
Past the SmallGroups library coverage — no SmallGroups id.