Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C283 ⋊ #355 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4528 |
Polycyclic presentation:
2^6,283|a^2=d,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^282,c^b=cf,d^b=def,d^c=df1987 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49119409, #49119410, #49119417, … |
| maximal normal subgroup of | #49119409, #49119410, #49119417, … |
| maximal quotient of | #49119193, #49119205, #49119264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 346);