Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C4×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ #2321 |
808 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=g,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^12284 conjugacy classes — view the full character table.
| maximal subgroup of | #15758452, #15758454, #15758462, … |
| maximal normal subgroup of | #15758452, #15758454, #15758462, … |
| maximal quotient of | #15784157, #15784198, #15784221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7164);