Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | C22×#11713272 |
| Fitting | C22×C4×#120 ⋊ D3 |
52734 conjugacy classes of subgroups; only the 688 normal subgroups are shown.
This group has 52734 conjugacy classes of subgroups — too many to draw. Only its 688 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D4×#1020⋊C2 |
| maximal normal subgroup of | C22×D4×#1020⋊C2 |
| maximal quotient of | C2×#72240986 |
Past the SmallGroups library coverage — no SmallGroups id.