Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×D4×C281 ⋊ C2 |
| Sylow | C281 ⋊ #459 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8992 |
Polycyclic presentation:
2^6,281|b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^280,e^c=ef2819 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49094357, #49094359, #49094368, … |
| maximal normal subgroup of | #49094357, #49094359, #49094368, … |
| maximal quotient of | #49094644, #49094658, #49094668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 744);