Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C13×#322 ⋊ C2 |
| Sylow | C13 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 121 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=d,b^2=e,d^2=f,e^2=g,c^a=cf,h^b=h^12,h^c=h^12320 conjugacy classes — view the full character table.
| maximal subgroup of | C8×M16×D13, C2×#13113115, #15828500, … |
| maximal normal subgroup of | C8×M16×D13, C2×#13113115, #15828500, … |
| maximal quotient of | #15752271, #15752299, #15753343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2789);