Finite Group DatabasebetaFinite Group Databasebeta| order | 8640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 110592 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C8 |
| abelian | C5×C82×C27 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C42×C9 | C22×C3×C5 |
| socle, prime radical | C22×C3×C5 | C42×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
296 conjugacy classes of subgroups.
8640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C8×C16×C27, C2×C5×C82×C27, C5×C82×C81, … |
| maximal normal subgroup of | C5×C8×C16×C27, C2×C5×C82×C27, C5×C82×C81, … |
| maximal quotient of | C5×C8×C16×C27, C2×C5×C82×C27, C5×C82×C81, … |
Past the SmallGroups library coverage — no SmallGroups id.