Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C283 ⋊ C2 |
| Sylow | C283 ⋊ #508 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^282,d^b=de,e^b=ef,g^b=g^282,g^c=g^2821573 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49123569, #49123571, #49123575, … |
| maximal normal subgroup of | #49123569, #49123571, #49123575, … |
| maximal quotient of | #49122967, #49123042, #49123107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 982);