Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C13×#498 ⋊ C2 |
| Sylow | C13 ⋊ #1671 |
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=d,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,e^c=eg,h^c=h^12161 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1671, C2×#13114208, #15845184, … |
| maximal normal subgroup of | D13×#1671, C2×#13114208, #15845184, … |
| maximal quotient of | #15755960, #15759061, #15759075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 3882);