Finite Group DatabasebetaFinite Group Databasebeta| order | 11970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#14558802 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C19 | C2×C9 |
| prime radical | C5⋊((C19⋊C3)⋊D7) | C3 |
| cosocle | C5×C7×C19⋊C3 | C2×C3 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,7,19|b^3=c^2,d^a=d^4,e^a=e^6,f^a=f^18,e^b=e^2,f^b=f^16,f^c=f^786 conjugacy classes — view the full character table.
| maximal subgroup of | #14558808⋊D5, #14558804⋊D5, D5×#14558802, … |
| maximal normal subgroup of | #14558808⋊D5, #14558804⋊D5, D5×#14558802, … |
| maximal quotient of | #37561073, C2×C5⋊#14558802 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11970, 65);