Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33×C4 |
| direct product | C2×C32×C42⋊C3 |
| unambiguous semidirect product | (C2×C42)⋊C33 |
| unambiguous semidirect product | (C2×C3×C42)⋊C32 |
| Fitting | C2×C32×C42 ⋊ C3 |
| derived | C42 ⋊ C2×C33 |
| Sylow | C2×C42 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C42⋊C3 |
| commutator, cosocle, hypocenter | C42 | C2×C33 |
| Frattini | C22 | C2×C32×A4 |
| Fitting | C2×C32×C42 | C3 |
| socle | C23×C32 | A4 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C2×C32 | |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#4623, C3×C3⋊#4623, C3⋊(C3⋊#4623), … |
| maximal normal subgroup of | C32×#4623, C3×C3⋊#4623, C3⋊(C3⋊#4623), … |
| maximal quotient of | C32×C4×C42⋊C3, C2×C32×#95⋊C3, C32×#376⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3697);