Finite Group DatabasebetaFinite Group Databasebeta| order | 17136 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 110592 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C7×C9×C17 |
| multiplicative | (ℤ/22705)ˣ, (ℤ/26529)ˣ, (ℤ/26709)ˣ, (ℤ/32145)ˣ, (ℤ/32265)ˣ, (ℤ/34288)ˣ, (ℤ/35372)ˣ, (ℤ/35612)ˣ, (ℤ/42860)ˣ, (ℤ/45410)ˣ, (ℤ/53058)ˣ, (ℤ/53418)ˣ, (ℤ/64290)ˣ, (ℤ/64530)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C3×C7×C17 |
| socle, prime radical | C23×C3×C7×C17 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
17136 conjugacy classes. The character table is too large to display.
| automorphism group of | C5×C27×C239 |
| outer automorphism group of | C5×C27×C239 |
Past the SmallGroups library coverage — no SmallGroups id.