Finite Group DatabasebetaFinite Group Databasebeta| order | 16900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C13 |
| direct product | D25×C13⋊D13 |
| unambiguous semidirect product | (C13×D25)⋊D13 |
| Fitting, derived, Hall | C132×C25 ⋊ C22 |
| Sylow | C132 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C132×C25 | C22 |
| Frattini | C5 | D5×C13⋊D13 |
| socle | C5×C132 | C2×D5 |
| LCS | G ▷ C132×C25 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4225 |
1204 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16900, 78);