Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C281 ⋊ C2 |
| Sylow | C281 ⋊ #418 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4496 |
Polycyclic presentation:
2^6,281|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^280,c^b=cf,d^b=df,g^b=g^2802822 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49095272, #49095274, #49095677, … |
| maximal normal subgroup of | #49095272, #49095274, #49095677, … |
| maximal quotient of | #49093695, #49093721, #49093747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 555);