Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11762772 |
| Fitting | C22×M16×C17 ⋊ C2 |
| Sylow | C17 ⋊ C2×#407 |
1008 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16939554, #16939561, #16939564, … |
| maximal normal subgroup of | #16939554, #16939561, #16939564, … |
| maximal quotient of | C2×#14527110, C2×#14527113, C2×#14527116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12945);