Finite Group DatabasebetaFinite Group Databasebeta| order | 7980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D35×D57 |
| 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.
570 conjugacy classes — view the full character table.
| maximal subgroup of | D35×D171, #37561375, #37561376, … |
| maximal normal subgroup of | #37561375, #37561376, D57×C5⋊AGL(1,𝔽7), … |
| maximal quotient of | D35×D171, C3×D35×D57, D57×D105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7980, 158);