Finite Group DatabasebetaFinite Group Databasebeta| order | 11970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#11716326 |
| unambiguous semidirect product | C3⋊(C5×#11716326) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊#11716326 |
| commutator, cosocle, hypocenter | C3×C7×C19 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C19 | C2×C3 |
| LCS | G ▷ C3×C7×C19 | |
| UCS | C1 ◁ C5 | |
72 conjugacy classes of subgroups.
420 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11970, 116);