Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C281 ⋊ #491 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17984 |
Polycyclic presentation:
2^6,281|a^2=f,b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^280,c^b=cf,g^b=g^280,g^c=g^2801976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49094626, #49094627, #49094631, … |
| maximal normal subgroup of | #49094626, #49094627, #49094631, … |
| maximal quotient of | #49095436, #49095992, #49096122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 919);