Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #2369 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,h^b=h^12290 conjugacy classes — view the full character table.
| maximal subgroup of | #15757375, #15757377, #15757379, … |
| maximal normal subgroup of | #15757375, #15757377, #15757379, … |
| maximal quotient of | C4⋊C4×C4⋊Dic13, #15784464, #15784468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7599);