Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C210 |
| direct product | C2×#72234951 |
| Fitting, Sylow | C2×#10586813 ⋊ C3 |
| derived | #62694 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72234951 |
| commutator, cosocle, hypocenter | #62694 | C22×C3 |
| Frattini | C22 | C22×C22⋊(C22⋊A4) |
| Fitting | C2×#10586813 | C3 |
| socle | C23 | C2×C22⋊(C22⋊A4) |
| LCS | G ▷ #62694 | |
| UCS | C1 ◁ C2 | |
At least 9212 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has at least 9212 conjugacy classes of subgroups — too many to draw. Only its 227 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
100 conjugacy classes — view the full character table.
| maximal subgroup of | #72261808 |
| maximal normal subgroup of | #72261808 |
Past the SmallGroups library coverage — no SmallGroups id.