Finite Group DatabasebetaFinite Group Databasebeta| order | 16450 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C47 · Schur multiplier (H2) = C1 |
| direct product | C5×C47×D35 |
| unambiguous semidirect product | C5⋊(C5×D7×C47) |
| unambiguous semidirect product | C7⋊(C5×D5×C47) |
| Fitting, socle, Hall | C52×C7×C47 ⋊ C2 |
| derived | C5×C7 ⋊ C2×C5×C47 |
| Hall | C52×C47 ⋊ D7 |
| Hall | C7×C47 ⋊ C5×D5 |
| Hall | C52×C7 ⋊ C2×C47 |
| Sylow | C52 ⋊ D7×C47 |
| Sylow | C7 ⋊ C5×D5×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C47 | D35 |
| commutator, cosocle, hypocenter | C5×C7 | C2×C5×C47 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C47 | C2 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C5×C47 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3290 |
4465 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D35×D47, C5×D5×D7×C47, C5×D35⋊D47, … |
| maximal normal subgroup of | C5×D35×D47, C5×D5×D7×C47, C5×D35⋊D47, … |
| maximal quotient of | C5×C47×Dic35, C2×C5×C47×D35 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16450, 15);