Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #100×C281 ⋊ C2 |
| Sylow | C281 ⋊ #455 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4496 |
Polycyclic presentation:
2^6,281|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^280,d^b=df,e^b=ef,g^b=g^280,d^c=df1556 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49097294, #49097295, #49097305, … |
| maximal normal subgroup of | #49097294, #49097295, #49097305, … |
| maximal quotient of | #49094257, #49094262, #49094285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 729);