Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C42×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #126 |
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 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=e,c^2=f,b^a=bf,c^a=cef,g^a=g^2,h^a=h^2,g^d=gh106 conjugacy classes — view the full character table.
| maximal subgroup of | #13147792, #13147797, #13147800, … |
| maximal normal subgroup of | #13147792, #13147797, #13147800, … |
| maximal quotient of | #10592357⋊C3, #13141347, #13141349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1354);