Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ #2935 |
492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,f^2=g,b^a=be,d^b=dg,d^c=dg,h^d=h^12290 conjugacy classes — view the full character table.
| maximal subgroup of | #15833800, #15833803, #15833837, … |
| maximal normal subgroup of | #15833800, #15833803, #15833837, … |
| maximal quotient of | #15834672, #15834680, #15834691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13249);