Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#88129 |
| Fitting | C43×C13 ⋊ C2 |
| Sylow | C13 ⋊ C4×#124 |
652 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15750886, #15750959, #15750962, … |
| maximal normal subgroup of | #15750886, #15750959, #15750962, … |
| maximal quotient of | C4×#11718601, C4×#11718600, C4×#11718590, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7054);