Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#88141 |
| Sylow | C13 ⋊ C42×Q8 |
684 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15753515, #15753525, #15753535, … |
| maximal normal subgroup of | #15753515, #15753525, #15753535, … |
| maximal quotient of | C4×#11718310, C4×C4⋊C4×Dic13, #15784091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6859);