Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#11763922 |
| Fitting | C22×C4×C17 ⋊ C8 |
| Sylow | C17 ⋊ C2×#431 |
528 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 215 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #17981562, #17981563, C2×#14545787, … |
| maximal normal subgroup of | #17981562, #17981563, C2×#14545787, … |
| maximal quotient of | C2×#14545918, C2×C4×C22⋊#3633, C2×C4×C4⋊#3633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21748);