Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×#3622 |
| Sylow | C17 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16924881, #100×#3622, #16924886, … |
| maximal normal subgroup of | #16924881, #100×#3622, #16924886, … |
| maximal quotient of | #97×#3622, #16923705, #16924749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2788);