Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C4⋊#3633 |
| unambiguous semidirect product | #595⋊(C4⋊C8) |
| Fitting | C42×C17 ⋊ C8 |
| Sylow | C17 ⋊ C4×C4⋊C8 |
316 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #17981067, #17981068, #17981076, … |
| maximal normal subgroup of | #17981067, #17981068, #17981076, … |
| maximal quotient of | C8×C4⋊#3633, #17981623, #17981625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21647);