Finite Group DatabasebetaFinite Group Databasebeta| order | 15232 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C16×C32 (order 6144) · Inn(G) = C1 · Out(G) = C22×C3×C16×C32 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C15232 |
| abelian | C7×C17×C128 |
| multiplicative | (ℤ/15233)ˣ, (ℤ/30466)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C64 | C2×C7×C17 |
| socle, prime radical | C2×C7×C17 | C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
32 conjugacy classes of subgroups.
15232 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.