Finite Group DatabasebetaFinite Group Databasebeta| order | 11168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C349 ⋊ M32 |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,349|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^213,f^b=f^348,f^c=f^348716 conjugacy classes — view the full character table.
| maximal subgroup of | #36375034, #36375035, #36375060, … |
| maximal normal subgroup of | #36375034, #36375035, #36375060, … |
| maximal quotient of | #36375033, #36375039, #36375065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11168, 221);