Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#467 ⋊ C2 |
| Sylow | C13 ⋊ #3063 |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^b=h^12,d^c=dg,h^c=h^12,h^d=h^12164 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3063, C2×#13124526, #16730171, … |
| maximal normal subgroup of | D13×#3063, C2×#13124526, #16730171, … |
| maximal quotient of | #15846413, #15846435, #15846457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14200);