Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #2322 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=g,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^12,c^b=ce,h^b=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15778063, #15778895, #15868916, … |
| maximal normal subgroup of | #15778063, #15778895, #15868916, … |
| maximal quotient of | #15784163, #15784199, #15784216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7182);