Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C23×C43 |
| direct product | C4×#11709219 |
| Fitting, Sylow | C4×#13827 ⋊ C3 |
| derived | #13827 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #11709219 |
| commutator, hypocenter | #13827 | C3×C4 |
| Frattini, socle | C25 | C2×C22⋊A4 |
| Fitting | C4×#13827 | C3 |
| prime radical | C2×#11709219 | C2 |
| cosocle | C2×#13827 | C2×C3 |
| LCS | G ▷ #13827 | |
| UCS | C1 ◁ C4 | |
8992 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 8992 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #72260019 |
Past the SmallGroups library coverage — no SmallGroups id.