Finite Group DatabasebetaFinite Group Databasebeta| order | 21600 |
| isoclinism | isoclinic class of A5×A6 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C22×C3 |
| direct product | A5×A6 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
286 conjugacy classes of subgroups; only the 4 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 4 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
35 conjugacy classes — view the full character table.
| maximal quotient of | A5×SL(2,𝔽9), SL(2,𝔽5)×A6, #72228181, … |
Past the SmallGroups library coverage — no SmallGroups id.