Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊(#127⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C4 |
| direct product | C3×C3⋊(#127⋊C3) |
| unambiguous semidirect product | C3⋊(C3×#127⋊C3) |
| unambiguous semidirect product | #874⋊C32 |
| unambiguous semidirect product | (C3×#874)⋊C3 |
| Fitting | C32×C42 ⋊ C2×C3 |
| derived | C3×C42 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(#127⋊C3) |
| commutator, cosocle, hypocenter | C3×C42 | C2×C32 |
| Frattini | C22 | C3×D3×A4 |
| Fitting | C32×C42 | C2×C3 |
| socle | C22×C32 | C2×A4 |
| LCS | G ▷ C3×C42 | |
| UCS | C1 ◁ C3 | |
164 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#857⋊D3, #13165996, D3×C3⋊(#127⋊C3), … |
| maximal normal subgroup of | C3×#857⋊D3, #13165996, D3×C3⋊(#127⋊C3), … |
| maximal quotient of | C3×C3⋊(#392⋊C3), C3×C3⋊(#399⋊C3), C3×C3⋊(#384⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3017);