Finite Group DatabasebetaFinite Group Databasebeta| order | 10635 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C709⋊C3 |
| unambiguous semidirect product | C709⋊(C3×C5) |
| unambiguous semidirect product | (C5×C709)⋊C3 |
| Fitting, socle, Hall | C5×C709 ⋊ C3 |
| derived, Sylow | C709 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C709⋊C3 |
| commutator, cosocle, hypocenter | C709 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C709 | C3 |
| LCS | G ▷ C709 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
1195 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C709⋊C3, C5×D709⋊C3, D5×C709⋊C3, … |
| maximal normal subgroup of | C2×C5×C709⋊C3, C5×D709⋊C3, D5×C709⋊C3, … |
| maximal quotient of | C2×C5×C709⋊C3, C5×C709⋊C9, C3×C5×C709⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10635, 1);