Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of Dic34 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C4×#63218 |
| Fitting | C2×C4×C8×C17 ⋊ C2 |
| Sylow | C17 ⋊ C2×C4×M16 |
656 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 357 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16923704, #16923711, #16923716, … |
| maximal normal subgroup of | #16923704, #16923711, #16923716, … |
| maximal quotient of | C2×C8×#63218, C2×#14527070, C2×#14527078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12916);