Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#11718616 |
| Fitting | C22×C13×C22⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ C2×#379 |
3464 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 429 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15768179, #15768215, #15769236, … |
| maximal normal subgroup of | #15768179, #15768215, #15769236, … |
| maximal quotient of | C2×#13113057, C2×#13113058, C4×#11718616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6877);