Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×#595 |
| unambiguous semidirect product | D17⋊C43 |
| Fitting | C2×C42×C17 ⋊ C4 |
| derived, Sylow | C17 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #595 |
| commutator, hypocenter | C17 | C2×C43 |
| Frattini | C22 | C23×#595 |
| Fitting | C2×C42×C17 | C4 |
| socle | C23×C17 | C22×C4 |
| prime radical | C23×D17 | C23 |
| cosocle | C22×D17 | C24 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C42 | |
1272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543611, #17950370, #17950377, … |
| maximal normal subgroup of | C2×#14543611, #17950370, #17950377, … |
| maximal quotient of | C43×#595, C2×#95×#595, C2×C4×(C2×#595)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20935);