Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C281 ⋊ #443 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4496 |
Polycyclic presentation:
2^6,281|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^280,d^b=df,g^c=g^2801988 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49097181, #49097184, #49097186, … |
| maximal normal subgroup of | #49097181, #49097184, #49097186, … |
| maximal quotient of | D8×#14555886, SD16×#14555886, Q16×#14555886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 666);