Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #100 |
253 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^5,3^3|b^2=c,c^2=e,b^a=bd,c^a=ce,f^a=f^2,g^a=g^2,d^b=de,g^f=gh73 conjugacy classes — view the full character table.
| maximal subgroup of | #13139176, #13139177, #13139178, … |
| maximal normal subgroup of | #13139176, #13139177, #13139178, … |
| maximal quotient of | #13135760, #13135766, #13135798, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 527);