Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#10587670 |
| Sylow | C17 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 101 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 | #17981202, #17981204, #17981247, … |
| maximal normal subgroup of | #17981202, #17981204, #17981247, … |
| maximal quotient of | C8×#10587670, #17981831, #17981846, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21668);