Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C27 ⋊ C2 |
| Sylow | C27 ⋊ #126 |
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|b^2=d,c^2=e,f^3=g,g^3=h,b^a=be,c^a=cd,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,c^b=ce144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720147, #13136251, #13136252, … |
| maximal normal subgroup of | C2×#11720147, #13136251, #13136252, … |
| maximal quotient of | #13134158, C27⋊#401, #13134170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 114);