Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×#72209717 |
| Fitting, Sylow | C2×#6499867 ⋊ C3 |
| derived | #62817 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23 | #85645 |
| commutator, cosocle, hypocenter | #62817 | C22×C3 |
| Frattini | C24 | C22×C22⋊A4 |
| Fitting | C2×#6499867 | C3 |
| LCS | G ▷ #62817 | |
| UCS | C1 ◁ C23 | |
49023 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 49023 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 32 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72209720, C2×#72216913, C2×#72216969, … |
| maximal normal subgroup of | C2×#72209720, C2×#72216913, C2×#72216969, … |
| maximal quotient of | C2×#72227295 |
Past the SmallGroups library coverage — no SmallGroups id.