Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C27 · Schur multiplier (H2) = C4 |
| direct product | C2×C42⋊C27 |
| unambiguous semidirect product | (C2×C42)⋊C27 |
| derived | C42 ⋊ C2×C27 |
| Sylow | C2×C42 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C42⋊C3 |
| commutator, hypocenter | C42 | C2×C27 |
| Frattini | C22×C9 | C2×A4 |
| Fitting | C2×C42×C9 | C3 |
| socle, prime radical | C23×C3 | C22⋊C9 |
| cosocle | C42×C9 | C2×C3 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C2×C9 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13134128, C4×C42⋊C27, #383⋊C27, … |
| maximal normal subgroup of | #13134128, C4×C42⋊C27, #383⋊C27, … |
| maximal quotient of | C4×C42⋊C27, C2×#95⋊C27, #376⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 77);