Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C13×#126 ⋊ C2 |
| Sylow | C13 ⋊ #2723 |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=ef,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^12200 conjugacy classes — view the full character table.
| maximal subgroup of | #16070348, #16070361, #16070465, … |
| maximal normal subgroup of | #16070348, #16070361, #16070465, … |
| maximal quotient of | #15790480, #15790644, #15790659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 11425);