Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1088⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ C4⋊C8 |
101 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=d,d^2=e,b^a=bc,f^a=f^2,g^a=gh,h^a=h^2,f^b=gh^2,g^b=fh^2,h^b=h^2,f^c=f^2,g^c=g^2h^2,g^f=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | #6249⋊C8, SU(3,𝔽2)⋊C8, #13146176, … |
| maximal normal subgroup of | #6249⋊C8, SU(3,𝔽2)⋊C8, #13146176, … |
| maximal quotient of | #13136655, #13136656, #13136670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 660);