Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3×C5 |
| direct product | C2×#14268357 |
| Fitting | C23×C32×C52 ⋊ C2 |
| Hall | C32×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ C2×#638 |
| Sylow | C32 ⋊ C2×C22⋊(C5⋊D5) |
1296 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 395 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1800 |
906 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊D5×#638, C2×C3⋊D3×C22⋊(C5⋊D5), C2×D4×C3⋊(C3⋊(C5⋊D5)) |
| maximal normal subgroup of | C2×C5⋊D5×#638, C2×C3⋊D3×C22⋊(C5⋊D5), C2×D4×C3⋊(C3⋊(C5⋊D5)) |
Past the SmallGroups library coverage — no SmallGroups id.