Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C283 ⋊ #391 |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18112 |
Polycyclic presentation:
2^6,283|a^2=f,b^2=def,c^2=e,b^a=bd,c^a=ce,g^a=g^282,g^b=g^2822848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49119387, #49121220, #49121222, … |
| maximal normal subgroup of | #49119387, #49121220, #49121222, … |
| maximal quotient of | #49119490, #49119493, #49119514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 456);