Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #2633 |
512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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,c^2=e,d^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^12272 conjugacy classes — view the full character table.
| maximal subgroup of | #15758910, #15758912, #15763799, … |
| maximal normal subgroup of | #15758910, #15758912, #15763799, … |
| maximal quotient of | #15789403, #15789577, #15789657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 10378);