Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C28 · Schur multiplier (H2) = C227 |
| direct product | C22×D3×#3484 |
| Fitting | C22×C3×#3484 ⋊ C2 |
| Sylow | C3 ⋊ C23×#3484 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C25×D3 |
| commutator, cosocle | C22×C3 | C28 |
| Frattini | C22 | C27×D3 |
| Fitting | C22×C3×#3484 | C2 |
| socle | C24×C3 | C26 |
| hypercenter | C22×#3484 | D3 |
| hypocenter | C3 | C23×#3484 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C22×#3484 | |
Only the 476199 normal subgroups are shown; non-normal subgroups are omitted.
528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#72210469, D3×#72210511, D3×#72210555, … |
| maximal normal subgroup of | D3×#72210469, D3×#72210511, D3×#72210555, … |
Past the SmallGroups library coverage — no SmallGroups id.