Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q16×C283 ⋊ C2 |
| Sylow | C283 ⋊ #473 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|a^2=f,b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,e^c=ef,g^c=g^2821990 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49123229, #49123231, #49123236, … |
| maximal normal subgroup of | #49123229, #49123231, #49123236, … |
| maximal quotient of | #49120623, #49120628, #49120647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 821);