Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C277 ⋊ C4 |
| Sylow | C277 ⋊ #104 |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^217,c^b=ce,f^b=f^276,f^d=f^276359 conjugacy classes — view the full character table.
| maximal subgroup of | D277⋊#104, C2×#22579945, #31800999, … |
| maximal normal subgroup of | D277⋊#104, C2×#22579945, #31800999, … |
| maximal quotient of | #31800850, Q8⋊#14555667, #31800854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 211);