Finite Group DatabasebetaFinite Group Databasebeta| order | 13824 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | D3×#72215293 |
| Fitting | C26×C3 ⋊ C2×D32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×S42 |
| commutator, cosocle | C2×C3×A42 | C24 |
| Fitting | C26×C3 | C2×D32 |
| socle | C25×C3 | C22×D32 |
| hypercenter | C22 | D3×S42 |
| hypocenter | C3×A42 | C22×D4 |
| LCS | G ▷ C2×C3×A42 ▷ C3×A42 | |
| UCS | C1 ◁ C2 ◁ C22 | |
At least 16088 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
192 conjugacy classes — view the full character table.
| holomorph of | C3×SL(2,ℤ/4), C2×C3×S4 |
Past the SmallGroups library coverage — no SmallGroups id.