Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#11719393 |
| Fitting | C2×C13×#125 ⋊ C2 |
| Sylow | C13 ⋊ C2×#533 |
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #15754398, #15828932, #15829051, … |
| maximal normal subgroup of | #15754398, #15828932, #15829051, … |
| maximal quotient of | C2×#13117242, C2×#13117309, C2×#13117317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17800);