Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C521 ⋊ C4 |
| Sylow | C521 ⋊ #107 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4168 |
Polycyclic presentation:
2^5,521|a^2=d,b^2=ce,c^2=e,b^a=bc,c^a=ce,f^a=f^235,f^d=f^5201054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45688344, #45688345, #45688358, … |
| maximal normal subgroup of | #45688344, #45688345, #45688358, … |
| maximal quotient of | #45688295, #45688296, #45688306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 215);