Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ C8×#41 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^a=h^5,h^c=h^8,h^f=h^12140 conjugacy classes — view the full character table.
| maximal subgroup of | #16780529, #16780535, #16780541, … |
| maximal normal subgroup of | #16780529, #16780535, #16780541, … |
| maximal quotient of | #117×#1057, #16797270, C4×#11719063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21314);