Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C13×C4⋊Q8 ⋊ C2 |
| Sylow | C13 ⋊ #3509 |
992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15754877, #15754881, #15755163, … |
| maximal normal subgroup of | #15754877, #15754881, #15755163, … |
| maximal quotient of | #16023063, #16023316, #16023368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18394);