Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C281 ⋊ Q64 |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17984 |
Polycyclic presentation:
2^6,281|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^2801559 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q64×D281, C2×#31823303, #49097610, … |
| maximal normal subgroup of | Q64×D281, C2×#31823303, #49097610, … |
| maximal quotient of | #49093483, #49093484, #49093502, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 389);