Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#11763895 |
| Fitting | C22×C4×C17 ⋊ C8 |
| Sylow | C17 ⋊ C2×#324 |
328 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #17981289, #17981290, C4×#11763895, … |
| maximal normal subgroup of | #17981289, #17981290, C4×#11763895, … |
| maximal quotient of | C2×#14545784, #17981515, #17981524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21621);