Finite Group DatabasebetaFinite Group Databasebeta| order | 11830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C13 |
| direct product | C5×C7⋊(C13⋊D13) |
| unambiguous semidirect product | C7⋊(C5×C13⋊D13) |
| unambiguous semidirect product | C13⋊(C5×D91) |
| Fitting, socle, Hall | C5×C7×C132 ⋊ C2 |
| derived, Hall | C7×C132 ⋊ C2×C5 |
| Hall | C5×C132 ⋊ D7 |
| Sylow | C132 ⋊ C5×D7 |
| Hall | C5×C7 ⋊ C13⋊D13 |
| Sylow | C7 ⋊ C5×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C7⋊(C13⋊D13) |
| commutator, cosocle, hypocenter | C7×C132 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C132 | C2 |
| LCS | G ▷ C7×C132 | |
| UCS | C1 ◁ C5 | |
128 conjugacy classes of subgroups.
2965 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D13×D91, C5×D7×C13⋊D13, D65⋊D91, … |
| maximal normal subgroup of | C5×D13×D91, C5×D7×C13⋊D13, D65⋊D91, … |
| maximal quotient of | C5×C7⋊#10621725, C2×C5×C7⋊(C13⋊D13), C3×C5×C7⋊(C13⋊D13), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11830, 22);