Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #1762 |
388 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 133 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=e,b^2=f,c^2=e,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^12,c^b=cg,h^c=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1762, C2×#13114663, #15860686, … |
| maximal normal subgroup of | D13×#1762, C2×#13114663, #15860686, … |
| maximal quotient of | #15753523, #15753533, #15753568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4337);