Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C521 ⋊ #131 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8336 |
Polycyclic presentation:
2^5,521|a^2=d,d^2=e,f^a=f^235,c^b=ce,f^b=f^520,f^c=f^520,f^d=f^520670 conjugacy classes — view the full character table.
| maximal subgroup of | #45688475, #45688476, #45688477, … |
| maximal normal subgroup of | #45688475, #45688476, #45688477, … |
| maximal quotient of | #45688397, #45688407, #45688439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 234);