Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×C4×#6129 |
| Fitting | C2×C4×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ C2×C4×#41 |
1728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15754292, #15828727, #15828729, … |
| maximal normal subgroup of | #15754292, #15828727, #15828729, … |
| maximal quotient of | C2×C4×#88131, C2×C4×#88146, C2×C4×#88135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17688);