Finite Group DatabasebetaFinite Group Databasebeta| order | 11830 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×D35 |
| unambiguous semidirect product | C5⋊(C132×D7) |
| unambiguous semidirect product | C7⋊(D5×C132) |
| Fitting, socle, Hall | C5×C7×C132 ⋊ C2 |
| derived, Hall | C5×C7 ⋊ C2×C132 |
| Hall | C7×C132 ⋊ D5 |
| Hall | C5×C132 ⋊ D7 |
| Sylow | C7 ⋊ D5×C132 |
| Sylow | C5 ⋊ C132×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | D35 |
| commutator, cosocle, hypocenter | C5×C7 | C2×C132 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C132 | C2 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C132 | |
128 conjugacy classes of subgroups.
3211 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D13×D35, D35×C13⋊D13, D5×C132×D7, … |
| maximal normal subgroup of | C13×D13×D35, D35×C13⋊D13, D5×C132×D7, … |
| maximal quotient of | C132×Dic35, C2×C132×D35, C3×C132×D35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11830, 18);