Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C281 ⋊ C2 |
| Sylow | C281 ⋊ #509 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4496 |
Polycyclic presentation:
2^6,281|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^280,d^b=de,e^b=ef,g^b=g^2802816 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49097200, #49097203, #49097250, … |
| maximal normal subgroup of | #49097200, #49097203, #49097250, … |
| maximal quotient of | #49097016, #49097020, #49097091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 987);