Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×(C2×#3633)⋊C4 |
| Fitting | C22×C4×C17 ⋊ C8 |
| Sylow | C17 ⋊ C2×#336 |
528 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #17981069, #17981079, #17981083, … |
| maximal normal subgroup of | #17981069, #17981079, #17981083, … |
| maximal quotient of | C2×(C2×#3633)⋊C8, #17981562, #17981563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21643);