Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C13×C22⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ #2490 |
560 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=eg,b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^12,c^b=cg278 conjugacy classes — view the full character table.
| maximal subgroup of | #15930989, #15930993, #15931049, … |
| maximal normal subgroup of | #15930989, #15930993, #15931049, … |
| maximal quotient of | #15784859, #15785400, #15786009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 8862);