Finite Group DatabasebetaFinite Group Databasebeta| order | 17425 |
| automorphism | ? |
| homology | Abelianization (H1) = C17×C25 · Schur multiplier (H2) = C1 |
| direct product | C17×C41⋊C25 |
| unambiguous semidirect product | C41⋊(C17×C25) |
| unambiguous semidirect product | (C17×C41)⋊C25 |
| derived, Sylow | C41 ⋊ C17×C25 |
| Hall | C17×C41 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | C41⋊C5 |
| commutator, hypocenter | C41 | C17×C25 |
| Frattini | C5 | C17×C41⋊C5 |
| Fitting, socle, prime radical | C5×C17×C41 | C5 |
| cosocle | C5×C41 | C5×C17 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C5×C17 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17425 |
1105 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17×C41⋊C25, C17×D41⋊C25, D17×C41⋊C25, … |
| maximal normal subgroup of | C2×C17×C41⋊C25, C17×D41⋊C25, D17×C41⋊C25, … |
| maximal quotient of | C2×C17×C41⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17425, 2);