Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C17⋊(D169⋊C3) |
| unambiguous semidirect product | (C2×C17)⋊(D169⋊C3) |
| unambiguous semidirect product | (C2×C169⋊C3)⋊D17 |
| unambiguous semidirect product | (C2×D2873)⋊C3 |
| Fitting | C2×C17×C169 ⋊ C2×C3 |
| derived, Hall | C17×C169 ⋊ C22×C3 |
| Hall | C2×D2873 ⋊ C3 |
| Hall | C17×C169⋊C3 ⋊ C22 |
| Hall | C169⋊C3 ⋊ C2×D17 |
| Sylow | C169 ⋊ C2×C3×D17 |
| Sylow | C17 ⋊ C2×D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C17⋊(D169⋊C3) |
| commutator, cosocle, hypocenter | C17×C169 | C22×C3 |
| Frattini | C13 | C2×C17⋊(D13⋊C3) |
| Fitting | C2×C17×C169 | C2×C3 |
| socle | C2×C13×C17 | D13⋊C3 |
| LCS | G ▷ C17×C169 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5746 |
1012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 22);