Finite Group DatabasebetaFinite Group Databasebeta| order | 11168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C349 ⋊ #108 |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,349|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^213,f^b=f^348,f^d=f^348710 conjugacy classes — view the full character table.
| maximal subgroup of | #36375058, #36375059, #36375072, … |
| maximal normal subgroup of | #36375058, #36375059, #36375072, … |
| maximal quotient of | #36375006, #36375007, #36375020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11168, 217);