Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2423 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^12206 conjugacy classes — view the full character table.
| maximal subgroup of | #15906772, #15906775, #15906817, … |
| maximal normal subgroup of | #15906772, #15906775, #15906817, … |
| maximal quotient of | #15784866, #15785383, #15785715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 8031);