Finite Group DatabasebetaFinite Group Databasebeta| order | 15255 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C4×C7×C9×C16 (order 8064) · Inn(G) = C1 · Out(G) = C2×C4×C7×C9×C16 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C15255 |
| abelian | C5×C27×C113 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C9 | C3×C5×C113 |
| socle, prime radical | C3×C5×C113 | C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16 conjugacy classes of subgroups.
15255 conjugacy classes. The character table is too large to display.
| derived subgroup of | D15255, Dic15255, C2×D15255 |
| Fitting subgroup of | D15255 |
| maximal subgroup of | C2×C5×C27×C113, D15255 |
| maximal normal subgroup of | C2×C5×C27×C113, D15255 |
| maximal quotient of | C2×C5×C27×C113 |
Past the SmallGroups library coverage — no SmallGroups id.