Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C13×SD16 ⋊ C2 |
| Sylow | C13 ⋊ #3323 |
402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=eg,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^12,c^b=cg,d^b=de,h^b=h^12,f^c=fg,h^d=h^12197 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3323, C2×#13127057, #16739878, … |
| maximal normal subgroup of | D13×#3323, C2×#13127057, #16739878, … |
| maximal quotient of | #15878524, #15879332, #15880210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 16731);