Finite Group DatabasebetaFinite Group Databasebeta| order | 7900 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×#1035 |
| Fitting, Hall | C25×C79 ⋊ C4 |
| derived, Sylow | C25 ⋊ C4×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | #1035 |
| commutator, hypocenter | C25 | C4×C79 |
| Frattini | C5 | AGL(1,𝔽5)×C79 |
| Fitting | C25×C79 | C4 |
| socle | C5×C79 | AGL(1,𝔽5) |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C79 | |
18 conjugacy classes of subgroups.
790 conjugacy classes — view the full character table.
| maximal subgroup of | #1035×C79⋊C3, C3×C79×#1035, C79×C3⋊#1035 |
| maximal normal subgroup of | #1035×C79⋊C3, C3×C79×#1035 |
| maximal quotient of | C3×C79×#1035, C79×C3⋊#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7900, 6);