Finite Group DatabasebetaFinite Group Databasebeta| order | 7155 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 22464 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3 |
| abelian | C3×C5×C9×C53 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C32×C5×C53 |
| socle, prime radical | C32×C5×C53 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
40 conjugacy classes of subgroups.
7155 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C5×C9×C53, C5×C92×C53, C3×C5×C27×C53, … |
| maximal normal subgroup of | C2×C3×C5×C9×C53, C5×C92×C53, C3×C5×C27×C53, … |
| maximal quotient of | C2×C3×C5×C9×C53, C5×C92×C53, C3×C5×C27×C53, … |
Past the SmallGroups library coverage — no SmallGroups id.