Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #2931 |
500 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 166 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=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^5,d^b=dg,h^c=h^8,h^d=h^12,h^f=h^1298 conjugacy classes — view the full character table.
| maximal subgroup of | #16780756, #16780765, #16780774, … |
| maximal normal subgroup of | #16780756, #16780765, #16780774, … |
| maximal quotient of | #16795817, #16795820, #16795822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21234);