Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ Q32 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=gh,h^a=h^2,c^b=cd,d^b=de,f^b=gh^2,g^b=fh^2,h^b=h^2,f^c=f^2,g^c=g^2h^2,g^f=gh37 conjugacy classes — view the full character table.
| maximal subgroup of | #13146453, #13146456, #13146458, … |
| maximal normal subgroup of | #13146453, #13146456, #13146458, … |
| maximal quotient of | #13136687, #13136688, C2×#11720692 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 659);