Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C43 |
| direct product | C2×#72222569 |
| Fitting, Sylow | C2×#153709 ⋊ C3 |
| derived | #153709 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11709197 |
| commutator, cosocle, hypocenter | #153709 | C2×C3 |
| Frattini | C25 | C2×C22⋊A4 |
| Fitting | C2×#153709 | C3 |
| socle | C26 | C22⋊A4 |
| LCS | G ▷ #153709 | |
| UCS | C1 ◁ C22 | |
12939 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 12939 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | #72238913, C2×#72238916, #72239011, … |
| maximal normal subgroup of | C2×#72238916, C2×#72228154, #72239184 |
Past the SmallGroups library coverage — no SmallGroups id.