Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#383 ⋊ C2 |
| Sylow | C13 ⋊ C4×#126 |
516 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 189 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=ef,c^2=e,d^2=g,b^a=be,c^a=cf,h^d=h^12224 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D13×#126, C2×#13117384, #16021413, … |
| maximal normal subgroup of | C4×D13×#126, C2×#13117384, #16021413, … |
| maximal quotient of | #15784072, #15784091, Dic13×#383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7058);