Finite Group DatabasebetaFinite Group Databasebeta| order | 11970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C5⋊#11716321) |
| unambiguous semidirect product | C5⋊(C3⋊#11716321) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C19 | C2×C3 |
| LCS | G ▷ C3×C5×C7×C19 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,7,19|c^a=c^2,d^a=d^4,f^a=f^18,e^b=e^2,f^b=f^7360 conjugacy classes — view the full character table.
| maximal subgroup of | #11716325⋊D15, #11716327⋊D15, D15×#11716321, … |
| maximal normal subgroup of | #11716325⋊D15, #11716327⋊D15, D15×#11716321, … |
| maximal quotient of | C3⋊#22547614, C2×C3⋊(C5⋊#11716321) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11970, 135);