Finite Group DatabasebetaFinite Group Databasebeta| order | 7910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D565 |
| unambiguous semidirect product | C5⋊(C7×D113) |
| Fitting, socle, Hall | C5×C7×C113 ⋊ C2 |
| derived, Hall | C5×C113 ⋊ C2×C7 |
| Hall | C7×C113 ⋊ D5 |
| Sylow | C113 ⋊ C7×D5 |
| Hall | C5×C7 ⋊ D113 |
| Sylow | C5 ⋊ C7×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D565 |
| commutator, hypocenter | C5×C113 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C113 | C2 |
| LCS | G ▷ C5×C113 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
1988 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#14555933, C7×#14555934, C7⋊#14555933, … |
| maximal normal subgroup of | C7×#14555933, C7×#14555934, C7⋊#14555933, … |
| maximal quotient of | C7×Dic565, C2×C7×D565, C3×C7×D565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7910, 7);