Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #103 |
231 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=c,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^2,d^b=de,g^f=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #13138013, #13138014, #13138017, … |
| maximal normal subgroup of | #13138013, #13138014, #13138017, … |
| maximal quotient of | #13135733, #13135797, #13135800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 499);