Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #123 |
429 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 88 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:
2^5,3^3|a^2=e,c^a=cd,f^a=f^2,g^a=g^2,c^b=ce,g^f=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #13135204, #13135775, #13135781, … |
| maximal normal subgroup of | #13135204, #13135775, #13135781, … |
| maximal quotient of | #13144290, #13144291, #13144292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1812);