Finite Group DatabasebetaFinite Group Databasebeta| order | 15147 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C5×C16×C27 (order 8640) · Inn(G) = C1 · Out(G) = C22×C5×C16×C27 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C15147 |
| abelian | C11×C17×C81 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C27 | C3×C11×C17 |
| socle, prime radical | C3×C11×C17 | C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
20 conjugacy classes of subgroups.
15147 conjugacy classes. The character table is too large to display.
| derived subgroup of | D15147, Dic15147, C2×D15147 |
| Fitting subgroup of | D15147 |
| maximal subgroup of | C2×C11×C17×C81, D15147 |
| maximal normal subgroup of | C2×C11×C17×C81, D15147 |
| maximal quotient of | C2×C11×C17×C81 |
Past the SmallGroups library coverage — no SmallGroups id.