Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×Q8×D68 |
| Fitting | C2×C4×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ C2×D4×Q8 |
1568 conjugacy classes of subgroups; only the 621 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 621 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16926050, #16926053, #16926066, … |
| maximal normal subgroup of | #16926050, #16926053, #16926066, … |
| maximal quotient of | C2×Q8×#63227, C2×C4⋊C4×D68, C2×Q8×C4⋊Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17985);