Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #63243 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C23×C22⋊#595 |
| unambiguous semidirect product | D17⋊(C22×C22⋊C4) |
| unambiguous semidirect product | (C2×#595)⋊C24 |
| Fitting | C25×C17 ⋊ C4 |
| Sylow | C17 ⋊ C23×C22⋊C4 |
4632 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #17949632, #17956693, #17956729, … |
| maximal normal subgroup of | #17949632, #17956693, #17956729, … |
| maximal quotient of | C23×(C2×#595)⋊C4, C22×C4×C22⋊#595, C22×#11763750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21481);