Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#88251 |
| Fitting | C2×C4×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15754310, #15754311, #15754317, … |
| maximal normal subgroup of | #15754310, #15754311, #15754317, … |
| maximal quotient of | C4×#11719191, C4×#11719250, C4×#11719503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17715);