Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×C521 ⋊ C4 |
| Sylow | C521 ⋊ #99 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4168 |
Polycyclic presentation:
2^5,521|a^2=d,b^a=bc,c^a=ce,f^a=f^235,d^b=de,f^d=f^5201051 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45688332, #45688333, #45688334, … |
| maximal normal subgroup of | #45688332, #45688333, #45688334, … |
| maximal quotient of | #45688275, #45688278, #45688283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 204);