Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#10587492 |
| Fitting | C23×C8×C17 ⋊ C2 |
| Sylow | C17 ⋊ C22×#102 |
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
568 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16939887, #16939891, #16940585, … |
| maximal normal subgroup of | #16939887, #16939891, #16940585, … |
| maximal quotient of | C22×#11762538, C2×#14527210, C2×#14527184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12997);