Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C521 ⋊ C2 |
| Sylow | C521 ⋊ #123 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8336 |
Polycyclic presentation:
2^5,521|c^2=d,b^a=bd,c^a=ce,f^b=f^5202614 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #123×D521, C2×#30659690, #45687941, … |
| maximal normal subgroup of | #123×D521, C2×#30659690, #45687941, … |
| maximal quotient of | #45687294, #45687306, #45687308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 128);