Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2974 |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,b^a=be,d^a=de,h^a=h^8,c^b=ceg,h^b=h^12,h^f=h^12110 conjugacy classes — view the full character table.
| maximal subgroup of | #16793220, #16793223, #16793225, … |
| maximal normal subgroup of | #16793220, #16793223, #16793225, … |
| maximal quotient of | #16797488, #16797490, #16797532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21369);