Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#542 ⋊ C2 |
| Sylow | C13 ⋊ #3224 |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|b^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^12158 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3224, C2×#13125924, #16734324, … |
| maximal normal subgroup of | D13×#3224, C2×#13125924, #16734324, … |
| maximal quotient of | #15872287, #15872690, #15873524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15598);