Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C4×C521 ⋊ C4 |
| Sylow | C521 ⋊ #117 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4168 |
Polycyclic presentation:
2^5,521|a^2=e,c^2=d,b^a=bd,f^a=f^235,f^e=f^5201060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45688299, #45688300, #45688303, … |
| maximal normal subgroup of | #45688299, #45688300, #45688303, … |
| maximal quotient of | #45688368, C4×C22⋊#14523438, C4×C4⋊#14523438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 225);