Finite Group DatabasebetaFinite Group Databasebeta| order | 16900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C13 |
| direct product | C2×C13⋊D325 |
| unambiguous semidirect product | (C2×C13)⋊D325 |
| unambiguous semidirect product | (C2×C25)⋊(C13⋊D13) |
| Fitting | C2×C132×C25 ⋊ C2 |
| derived, Hall | C132×C25 ⋊ C22 |
| Sylow | C132 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C13⋊D325 |
| commutator, cosocle, hypocenter | C132×C25 | C22 |
| Frattini | C5 | C2×C5⋊(C13⋊D13) |
| Fitting | C2×C132×C25 | C2 |
| socle | C2×C5×C132 | D5 |
| LCS | G ▷ C132×C25 | |
| UCS | C1 ◁ C2 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8450 |
4228 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16900, 81);