Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11763711 |
| Fitting | C23×C4×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#352 |
278 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11763711, #17960816, #17960818, … |
| maximal normal subgroup of | C4×#11763711, #17960816, #17960818, … |
| maximal quotient of | C2×#14543710, C2×#14543729, #17958287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20758);