Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#11719188 |
| Sylow | C13 ⋊ C2×#543 |
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
284 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15754730, #15754733, #15771867, … |
| maximal normal subgroup of | #15754730, #15754733, #15771867, … |
| maximal quotient of | C2×#13117448, C2×#13117450, C2×#13117564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17905);