Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C283 ⋊ #451 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|a^2=f,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^282,d^b=df2839 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49120216, #49120217, #49120221, … |
| maximal normal subgroup of | #49120216, #49120217, #49120221, … |
| maximal quotient of | #49120218, #49120235, #49120286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 705);