Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×#88146 |
| Fitting | C4×C13×C4⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ C4×#117 |
752 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15752445, #15752449, #15752493, … |
| maximal normal subgroup of | #15752445, #15752449, #15752493, … |
| maximal quotient of | C4×#11718309, C4×#11718327, C4×C4⋊C4×Dic13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6850);