Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #2365 |
552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^12,d^b=de290 conjugacy classes — view the full character table.
| maximal subgroup of | #15757342, #15757346, #15757349, … |
| maximal normal subgroup of | #15757342, #15757346, #15757349, … |
| maximal quotient of | C4⋊C4×C4⋊Dic13, #15784460, #15784491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7568);