Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #106 |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=c,d^2=e,b^a=bde,f^a=f^2,g^a=g^2,d^b=de,g^f=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #13137893, #13137895, #13137899, … |
| maximal normal subgroup of | #13137893, #13137895, #13137899, … |
| maximal quotient of | #13135795, #13135804, #13135820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 497);