Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #131 |
173 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=e,c^2=e,d^2=e,f^a=fg,g^a=fg^2h^2,c^b=ce,f^d=f^2,g^d=g^2h,g^f=gh70 conjugacy classes — view the full character table.
| maximal subgroup of | #13146449, #13146658, #13146659, … |
| maximal normal subgroup of | #13146449, #13146658, #13146659, … |
| maximal quotient of | #13147334, #13147335, #13147336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2418);