Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #108×C283 ⋊ C2 |
| Sylow | C283 ⋊ #444 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4528 |
Polycyclic presentation:
2^6,283|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^b=g^282,g^c=g^2821996 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49123151, #49123155, #49123158, … |
| maximal normal subgroup of | #49123151, #49123155, #49123158, … |
| maximal quotient of | #49120072, #49120079, #49120084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 670);