Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | #64113⋊C3 |
| Fitting | C2×C8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #135 |
239 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^3,3,2^2,3^2|b^2=f,c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^2,h^a=h^2,g^d=gh106 conjugacy classes — view the full character table.
| maximal subgroup of | #13135068, #13135077, #13135088, … |
| maximal normal subgroup of | #13135068, #13135077, #13135088, … |
| maximal quotient of | #10592382⋊C3, C4×#3746⋊C3, C4×#3744⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1472);