Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C281 ⋊ C2 |
| Sylow | C281 ⋊ #492 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8992 |
Polycyclic presentation:
2^6,281|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^280,g^b=g^2801982 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49093469, #49094375, #49094376, … |
| maximal normal subgroup of | #49093469, #49094375, #49094376, … |
| maximal quotient of | #49094891, #49094896, #49094901, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 923);