Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #63243 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C8×C22⋊#595 |
| Fitting | C22×C8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C8×C22⋊C4 |
384 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #17948683, #17948684, #17948695, … |
| maximal normal subgroup of | #17948683, #17948684, #17948695, … |
| maximal quotient of | C8×C22⋊#3624, C8×#10587543, #17951728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20242);