Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C22×C3×C5×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C22×C3×C5 | A5 |
| commutator, hypocenter | A5 | C22×C3×C5 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C22×C3×C5 | |
334 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C5×A5⋊C4, C22×C3×D5×A5 |
| maximal normal subgroup of | C2×C3×C5×A5⋊C4, C22×C3×D5×A5 |
| maximal quotient of | C2×C3×C5×#6732 |
Past the SmallGroups library coverage — no SmallGroups id.