Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C2×D3×#52004 |
| Fitting | C2×C3×#52004 ⋊ C2 |
| Sylow | C3 ⋊ C22×#52004 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C25×D3 |
| commutator, cosocle | C23×C3 | C27 |
| Frattini | C23 | C26×D3 |
| Fitting | C2×C3×#52004 | C2 |
| socle | C24×C3 | C26 |
| hypercenter | C2×#52004 | D3 |
| hypocenter | C3 | C22×#52004 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C2×#52004 | |
At least 8140 conjugacy classes of subgroups; only the 35503 normal subgroups are shown.
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#72210566, D3×#72210575, D3×#72210469 |
| maximal normal subgroup of | D3×#72210566, D3×#72210575, D3×#72210469 |
Past the SmallGroups library coverage — no SmallGroups id.