Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C28 |
| direct product | C2×#72260605 |
| Fitting, Sylow | C2×#10586400 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | #63048 | C22×C3 |
| Frattini | C22 | C22×C22⋊(C22⋊A4) |
| Fitting | C2×#10586400 | C3 |
| socle | C23 | C2×C22⋊(C22⋊A4) |
| LCS | G ▷ #63048 | |
| UCS | C1 ◁ C22×C4 | |
Only the 258 normal subgroups are shown; non-normal subgroups are omitted.
Only the group's 258 normal subgroups are shown; non-normal subgroups are omitted.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
136 conjugacy classes — view the full character table.
| maximal subgroup of | #72261456 |
| maximal normal subgroup of | #72261456 |
Past the SmallGroups library coverage — no SmallGroups id.