Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C216 |
| direct product | C2×D42×S4 |
| Fitting | C23×D42 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×S4 |
| commutator, cosocle | C22×A4 | C26 |
| Frattini | C22 | C25×S4 |
| Fitting | C23×D42 | D3 |
| socle | C25 | C24×D3 |
| hypercenter | C2×D42 | S4 |
| hypocenter | A4 | C22×D42 |
| LCS | G ▷ C22×A4 ▷ A4 | |
| UCS | C1 ◁ C23 ◁ C2×D42 | |
194289 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72247039 |
Past the SmallGroups library coverage — no SmallGroups id.