Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#11718734 |
| Fitting | C2×C13×#127 ⋊ C2 |
| Sylow | C13 ⋊ C2×#493 |
760 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | #15758193, #15758194, #15758196, … |
| maximal normal subgroup of | #15758193, #15758194, #15758196, … |
| maximal quotient of | C2×#13114426, C2×#13114441, C2×#13114443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14921);