Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#63011⋊C3 |
| Fitting, Sylow | C4×#63011 ⋊ C3 |
| derived | H(3,𝔽4) ⋊ C22×C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #63011⋊C3 |
| commutator, hypocenter | H(3,𝔽4) | C22×C3×C4 |
| Frattini, socle | C23 | C23×C22⋊A4 |
| Fitting | C4×#63011 | C3 |
| prime radical | C2×#63011⋊C3 | C2 |
| cosocle | C2×H(3,𝔽4) | C23×C3 |
| LCS | G ▷ H(3,𝔽4) | |
| UCS | C1 ◁ C4 | |
27611 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#72224760, C4×#72218857 |
| maximal normal subgroup of | C4×#72224760, C4×#72218857 |
Past the SmallGroups library coverage — no SmallGroups id.