Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#11718402 |
| Fitting | C2×C13×#99 ⋊ C2 |
| Sylow | C13 ⋊ C2×B(4,𝔽2) |
1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | #15780178, #15780180, #15780192, … |
| maximal normal subgroup of | #15780178, #15780180, #15780192, … |
| maximal quotient of | C2×#13113755, C2×#13113756, C2×#13113789, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13895);