Finite Group DatabasebetaFinite Group Databasebeta| order | 7980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D21×D95 |
| 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.
588 conjugacy classes — view the full character table.
| maximal subgroup of | D63×D95, #37561365, #37561366, … |
| maximal normal subgroup of | #37561365, #37561366, C3⋊AGL(1,𝔽7)×D95, … |
| maximal quotient of | D63×D95, C3×D21×D95, D21×D285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7980, 155);