Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #2933 |
502 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,f^2=g,b^a=be,h^a=h^5,d^c=dg,h^c=h^8,h^f=h^1292 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13131568, D13⋊#2933, #16808303, … |
| maximal normal subgroup of | C2×#13131568, D13⋊#2933, #16808303, … |
| maximal quotient of | #16796029, #16796035, #16796039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21242);