Finite Group DatabasebetaFinite Group Databasebeta| order | 35770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D511 |
| unambiguous semidirect product | C7⋊(C5×C7×D73) |
| unambiguous semidirect product | C73⋊(C5×C7×D7) |
| Fitting, socle, Hall | C5×C72×C73 ⋊ C2 |
| derived | C7×C73 ⋊ C2×C5×C7 |
| Hall | C72×C73 ⋊ C2×C5 |
| Hall | C5×C73 ⋊ C7×D7 |
| Hall | C5×C72 ⋊ D73 |
| Sylow | C73 ⋊ C5×C7×D7 |
| Sylow | C72 ⋊ C5×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D511 |
| commutator, cosocle, hypocenter | C7×C73 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C73 | C2 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C5×C7 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5110 |
8995 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35770, 12);