Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C281 ⋊ C2 |
| Sylow | C281 ⋊ #461 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8992 |
Polycyclic presentation:
2^6,281|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^280,e^c=ef,g^c=g^2802819 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49094483, #49094485, #49094504, … |
| maximal normal subgroup of | #49094483, #49094485, #49094504, … |
| maximal quotient of | #49094679, #49094693, #49094703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 755);