Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C13×Q16 ⋊ C2 |
| Sylow | C13 ⋊ #2951 |
484 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^b=h^12,d^c=dg,h^c=h^12,h^d=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #16016256, #16016260, #16016267, … |
| maximal normal subgroup of | #16016256, #16016260, #16016267, … |
| maximal quotient of | #15832400, #15832627, #15832771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13385);