Finite Group DatabasebetaFinite Group Databasebeta| order | 11830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C13 |
| direct product | D5×C132⋊C7 |
| unambiguous semidirect product | C5⋊(C2×C132⋊C7) |
| unambiguous semidirect product | (D5×C132)⋊C7 |
| Fitting, socle, derived, Hall | C5×C132 ⋊ C2×C7 |
| Hall | C5×C132⋊C7 ⋊ C2 |
| Hall | D5×C132 ⋊ C7 |
| Sylow | C132 ⋊ C7×D5 |
| Sylow | C5 ⋊ C2×C132⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C132 | C2×C7 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
124 conjugacy classes — view the full character table.
| maximal subgroup of | #37556829, AGL(1,𝔽5)×C132⋊C7, #16810007⋊C7, … |
| maximal normal subgroup of | #37556829, AGL(1,𝔽5)×C132⋊C7, #16810007⋊C7, … |
| maximal quotient of | Dic5×C132⋊C7, C2×D5×C132⋊C7, C3×D5×C132⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11830, 14);