Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ C4⋊C8 |
73 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=cde,d^2=e,b^a=bc,f^a=gh^2,g^a=f^2,f^b=f^2g^2,g^b=f^2gh^2,f^c=f^2h^2,g^c=g^2h,g^f=gh64 conjugacy classes — view the full character table.
| maximal subgroup of | #6249⋊C8, #13146168, (#1088⋊C2)⋊C8, … |
| maximal normal subgroup of | #6249⋊C8, #13146168, (#1088⋊C2)⋊C8, … |
| maximal quotient of | #13136722, #13136723, #13136728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 675);