Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#88132 |
| Sylow | C13 ⋊ C4×C22⋊Q8 |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#88132, #15870330, #15870340, … |
| maximal normal subgroup of | C8×#88132, #15870330, #15870340, … |
| maximal quotient of | C4×#11718611, C4×#11718607, C4×#11718316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7041);