Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#11763689 |
| Sylow | C17 ⋊ C2×#343 |
432 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | #17948859, #17948861, C4×#11763689, … |
| maximal normal subgroup of | #17948859, #17948861, C4×#11763689, … |
| maximal quotient of | C2×#14543622, #17950555, #17950558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20212);