Finite Group DatabasebetaFinite Group Databasebeta| order | 3240 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 776355840 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C36 |
| abelian | C2×C34×C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C34×C5 |
| socle, prime radical | C22×C34×C5 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3392 conjugacy classes of subgroups.
3240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C34×C5×C8, C34×C42×C5, C22×C34×C4×C5, … |
| maximal normal subgroup of | C2×C34×C5×C8, C34×C42×C5, C22×C34×C4×C5, … |
| maximal quotient of | C2×C34×C5×C8, C34×C42×C5, C22×C34×C4×C5, … |
Past the SmallGroups library coverage — no SmallGroups id.