Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×H(3,𝔽3) ⋊ C4 |
| Sylow | H(3,𝔽3) ⋊ #99 |
186 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=e,b^a=bd,d^a=de,f^a=fg,g^a=fg^2h^2,c^b=ce,f^c=f^2,g^c=g^2h,g^f=gh49 conjugacy classes — view the full character table.
| maximal subgroup of | #13136677, #13136678, #13136876, … |
| maximal normal subgroup of | #13136677, #13136678, #13136876, … |
| maximal quotient of | #13136876, #13136877, #13136878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 747);