Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C521 ⋊ C4 |
| Sylow | C521 ⋊ #103 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4168 |
Polycyclic presentation:
2^5,521|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^235,c^b=ce,f^d=f^520664 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#30659771, #45688422, #45688423, … |
| maximal normal subgroup of | C2×#30659771, #45688422, #45688423, … |
| maximal quotient of | Q8⋊#16861967, #45688282, #45688285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 209);