Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D17×#564 |
| Fitting | C17×#564 ⋊ C2 |
| Sylow | C17 ⋊ C2×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | C17×#564 | C2 |
| prime radical | C22×D17 | C24 |
| hypercenter | #564 | D17 |
| hypocenter | C17 | C2×#564 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #564 | |
896 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1658, D17×#1663, #17015624, … |
| maximal normal subgroup of | D17×#1658, D17×#1663, #17015624, … |
| maximal quotient of | D17×#2382, #17197044, #564×Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18652);