Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C13×#137 ⋊ C2 |
| Sylow | C13 ⋊ #3278 |
482 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,d^b=de,e^b=eg,h^c=h^12,e^d=eg161 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3278, C2×#13126496, #16738094, … |
| maximal normal subgroup of | D13×#3278, C2×#13126496, #16738094, … |
| maximal quotient of | #15854246, #15854362, #15854368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 16170);