Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | SD16×#3624 |
| Sylow | C17 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16×#3624, SD16×#63242, #135×#3624, … |
| maximal normal subgroup of | C2×SD16×#3624, SD16×#63242, #135×#3624, … |
| maximal quotient of | #102×#3624, #103×#3624, #106×#3624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20092);