Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#380 ⋊ C2 |
| Sylow | C13 ⋊ #2319 |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^12,h^c=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15830473, #15830476, #15830484, … |
| maximal normal subgroup of | #15830473, #15830476, #15830484, … |
| maximal quotient of | #15784187, #15784189, #15784205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7152);