Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
| direct product | C4×#10587542 |
| Sylow | C17 ⋊ C4×#97 |
360 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #17948239, #17948268, #17948270, … |
| maximal normal subgroup of | #17948239, #17948268, #17948270, … |
| maximal quotient of | C4×#11763651, C8×#10587542, #17950275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20165);