Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C4×C13×C22⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ #2361 |
788 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,d^b=de,h^b=h^12290 conjugacy classes — view the full character table.
| maximal subgroup of | #15883187, #15883196, #15883232, … |
| maximal normal subgroup of | #15883187, #15883196, #15883232, … |
| maximal quotient of | C22⋊C4×C4⋊Dic13, #15784417, #15784483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7524);