Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C26 |
| direct product | C2×#72209857 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #87588⋊C2 |
| commutator, cosocle, hypocenter | C22⋊#997 | C23 |
| Frattini | C23 | C22×#1020 |
| Fitting | C2×#35346 | D3 |
| socle | C24 | C2×#1020 |
| prime radical | C2×#35346⋊C3 | C2 |
| LCS | G ▷ C22⋊#997 | |
| UCS | C1 ◁ C22 | |
11728 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 11728 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
80 conjugacy classes — view the full character table.
| maximal quotient of | C2×#72246416 |
Past the SmallGroups library coverage — no SmallGroups id.