Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ #126 |
195 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^3,3,2^2,3^2|b^2=e,c^2=f,g^3=h,b^a=bf,c^a=cef,g^a=g^2h^2,h^a=h^2,g^d=gh106 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11721396, #10589581⋊C3, #10589633⋊C3, … |
| maximal normal subgroup of | C2×#11721396, #10589581⋊C3, #10589633⋊C3, … |
| maximal quotient of | #10588338⋊C3, #13141379, 3−1+2⋊#401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1363);