Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C521 ⋊ C2 |
| Sylow | C521 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8336 |
Polycyclic presentation:
2^5,521|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^520,d^b=de,f^c=f^5201831 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #137×D521, C2×#30659740, #45688229, … |
| maximal normal subgroup of | #137×D521, C2×#30659740, #45688229, … |
| maximal quotient of | #45687432, #45687439, #45687473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 178);