Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#10587544 |
| Sylow | C17 ⋊ C4×C4⋊C8 |
316 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 154 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 | #17948246, #17948249, #17948260, … |
| maximal normal subgroup of | #17948246, #17948249, #17948260, … |
| maximal quotient of | C8×#10587544, #17952264, #17952274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20293);