Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C4×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ #2361 |
788 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,h^a=h^12,d^b=de,h^d=h^12290 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2361, C2×#13117853, #16022478, … |
| maximal normal subgroup of | D13×#2361, C2×#13117853, #16022478, … |
| maximal quotient of | C22⋊C4×#6101, #15784414, #15784417, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7527);