Finite Group DatabasebetaFinite Group Databasebeta| order | 5408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C13 |
| direct product | D4×#10621729 |
| Fitting | D4×C132 ⋊ C4 |
| Sylow | C132 ⋊ C4×D4 |
350 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
230 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D13⋊#261, #72259270, #72259308, … |
| maximal normal subgroup of | D4×D13⋊#261, #72259270, #72259308, … |
Past the SmallGroups library coverage — no SmallGroups id.