Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C283 ⋊ C2 |
| Sylow | C283 ⋊ #436 |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^282,c^b=cf,g^b=g^2824540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49119218, #49119220, #49120090, … |
| maximal normal subgroup of | #49119218, #49119220, #49120090, … |
| maximal quotient of | #49120147, #49120153, #49120159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 628);