Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#14523438)⋊C4 |
| Fitting | C2×C4×C521 ⋊ C4 |
| Sylow | C521 ⋊ #95 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4168 |
Polycyclic presentation:
2^5,521|a^2=d,b^2=e,b^a=bc,f^a=f^235,f^d=f^5201060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45688283, #45688284, #45688285, … |
| maximal normal subgroup of | #45688283, #45688284, #45688285, … |
| maximal quotient of | #45688297, #45688298, #45688299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 197);