Finite Group DatabasebetaFinite Group Databasebeta| order | 7980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D19×D105 |
| unambiguous semidirect product | (C3×D19)⋊D35 |
| unambiguous semidirect product | (C5×D19)⋊D21 |
| unambiguous semidirect product | (C7×D19)⋊D15 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C7×C19 | C22 |
| LCS | G ▷ C3×C5×C7×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
594 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D315, #11716321⋊D15, #11716322⋊D15, … |
| maximal normal subgroup of | #11716321⋊D15, #11716322⋊D15, D19×C3⋊(C5⋊AGL(1,𝔽7)), … |
| maximal quotient of | D19×D315, C3×D19×D105, D57⋊D105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7980, 144);