Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×#72210936 |
| Fitting, Sylow | C2×#94877 ⋊ C3 |
| derived | #7014 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #1455⋊C3 |
| commutator, cosocle, hypocenter | #7014 | C22×C3 |
| Frattini | C43 | C22×A4 |
| Fitting | C2×#94877 | C3 |
| socle | C24 | C2×#95⋊C3 |
| LCS | G ▷ #7014 | |
| UCS | C1 ◁ C2×C4 | |
1389 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 1389 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.
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72211693 |
| maximal normal subgroup of | C2×#72211693 |
| maximal quotient of | C2×#72210939 |
Past the SmallGroups library coverage — no SmallGroups id.