Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#10587580 |
| Fitting | C22×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ C22×#123 |
1968 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 605 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16925671, #16926946, #16926962, … |
| maximal normal subgroup of | #16925671, #16926946, #16926962, … |
| maximal quotient of | C22×#11762671, C22×#11762680, C22×#11762687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17745);