Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C33×C4 |
No aliases for this group.
| Fitting | C33×C4⋊C4 ⋊ C2 |
| Sylow | C33 ⋊ #117 |
1064 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 327 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=e,c^2=d,c^a=ce,f^a=f^2,g^a=g^2,h^a=h^2,c^b=ce150 conjugacy classes — view the full character table.
| maximal subgroup of | #13159179, #13159180, #13159181, … |
| maximal normal subgroup of | #13159179, #13159180, #13159181, … |
| maximal quotient of | #13163286, #13163289, #13163293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3900);