Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C13×C22⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ #2480 |
664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|b^2=ef,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^12,c^b=cg278 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2480, C2×#13119082, #16030696, … |
| maximal normal subgroup of | D13×#2480, C2×#13119082, #16030696, … |
| maximal quotient of | #15784831, #15785129, #15785729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 8756);