Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | Q8×#6094 |
| Fitting | C8×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ Q8×M16 |
388 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15833837, #15833843, #15833848, … |
| maximal normal subgroup of | #15833837, #15833843, #15833848, … |
| maximal quotient of | C4⋊C4×#6094, #15861566, Q8×#88055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13460);