Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C27 ⋊ #104 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^5,3^3|a^2=c,c^2=e,d^2=e,f^3=g,g^3=h,b^a=bd,d^a=de,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,d^b=de144 conjugacy classes — view the full character table.
| maximal subgroup of | #104×D27, #13134326, #13134649, … |
| maximal normal subgroup of | #104×D27, #13134326, #13134649, … |
| maximal quotient of | #13134028, D4⋊(C27⋊C8), #13134031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 44);