Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#123 ⋊ C4 |
| Sylow | C13 ⋊ #2322 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
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^5,c^b=ce,h^b=h^8,h^g=h^1286 conjugacy classes — view the full character table.
| maximal subgroup of | #16789417, #16799827, C2×#13131322, … |
| maximal normal subgroup of | #16789417, #16799827, C2×#13131322, … |
| maximal quotient of | #16791564, #16791579, #16791583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20996);