Finite Group DatabasebetaFinite Group Databasebeta| order | 7910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C113⋊C7 |
| unambiguous semidirect product | (C2×C113)⋊(C5×C7) |
| unambiguous semidirect product | (C2×C5×C113)⋊C7 |
| Fitting, socle, Hall | C2×C5×C113 ⋊ C7 |
| derived, Sylow | C113 ⋊ C2×C5×C7 |
| Hall | C5×C113 ⋊ C2×C7 |
| Hall | C2×C113 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C113⋊C7 |
| commutator, hypocenter | C113 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C113 | C7 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C2×C5 | |
16 conjugacy classes of subgroups.
230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7910, 2);