Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#11718225 |
| Fitting | C2×C42×C13 ⋊ C4 |
| Sylow | C13 ⋊ C2×#353 |
368 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
122 conjugacy classes — view the full character table.
| maximal subgroup of | #16778100, #16778101, #16778120, … |
| maximal normal subgroup of | #16778100, #16778101, #16778120, … |
| maximal quotient of | C2×#13129765, C2×#13129778, #16786896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20777);