Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×D13×M32 |
| Fitting | C2×C13×M32 ⋊ C2 |
| Sylow | C13 ⋊ C22×M32 |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×#1375, #15777767, D13×#1376, … |
| maximal normal subgroup of | D13×#1375, #15777767, D13×#1376, … |
| maximal quotient of | C2×D13×#346, C4×D13×M32, C2×M32×Dic13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17604);