Finite Group DatabasebetaFinite Group Databasebeta| order | 11830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#14556975 |
| Fitting, socle, Hall | C5×C132 ⋊ D7 |
| derived, Hall | C5×C132⋊C7 ⋊ C2 |
| Hall | C132⋊C7 ⋊ D5 |
| Sylow | C132 ⋊ D35 |
| Sylow | C5 ⋊ #14556975 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C132⋊C7 | C2 |
| Fitting, socle | C5×C132 | D7 |
| LCS | G ▷ C5×C132⋊C7 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,13^2|b^a=b^4,c^a=c^6,d^a=d^2e,e^a=d^10e^11,d^c=d^6e^8,e^c=d^3e^297 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11830, 12);