Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C353 ⋊ C2 |
| Sylow | C353 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,353|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^352,d^b=de,f^c=f^3521243 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D353, C2×#26015019, #36378584, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D353, C2×#26015019, #36378584, … |
| maximal quotient of | #36377787, #36377790, #36377826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 173);