Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11763663 |
| Fitting | C22×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#328 |
336 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
118 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11763663, #17952050, #17952057, … |
| maximal normal subgroup of | C4×#11763663, #17952050, #17952057, … |
| maximal quotient of | C2×#14543603, C2×#14543604, #17949666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19880);