Finite Group DatabasebetaFinite Group Databasebeta| order | 7290 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3820252999680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C310 |
| abelian | C2×C34×C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C2×C35×C5 |
| socle, prime radical | C2×C35×C5 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
20464 conjugacy classes of subgroups.
7290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C34×C4×C5×C9, C22×C34×C5×C9, C2×C34×C5×C27, … |
| maximal normal subgroup of | C34×C4×C5×C9, C22×C34×C5×C9, C2×C34×C5×C27, … |
| maximal quotient of | C34×C4×C5×C9, C22×C34×C5×C9, C2×C34×C5×C27, … |
Past the SmallGroups library coverage — no SmallGroups id.