Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
| direct product | D4×#5936 |
13622 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 13622 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#1020⋊C4, D4×#73080, C4×D4×#1020 |
| maximal normal subgroup of | D4×#1020⋊C4, D4×#73080, C4×D4×#1020 |
| maximal quotient of | #72342126 |
Past the SmallGroups library coverage — no SmallGroups id.