Finite Group DatabasebetaFinite Group Databasebeta| order | 7708 |
| isoclinism | isoclinic class of D47 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C41 · Schur multiplier (H2) = C2 |
| direct product | C2×C41×D47 |
| unambiguous semidirect product | C47⋊(C22×C41) |
| unambiguous semidirect product | (C2×C47)⋊(C2×C41) |
| Fitting, socle | C2×C41×C47 ⋊ C2 |
| derived, Sylow | C47 ⋊ C22×C41 |
| Hall | C41×C47 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | D47 |
| commutator, hypocenter | C47 | C22×C41 |
| Frattini | C1 | G |
| Fitting, socle | C2×C41×C47 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C2×C41 | |
20 conjugacy classes of subgroups.
2050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C41×D47, C2×C3×C41×D47, C2×C41×D141, … |
| maximal normal subgroup of | C2×C3×C41×D47, C2×D47×C41⋊C5, C2×C5×C41×D47 |
| maximal quotient of | D3×C41×D47, C2×C3×C41×D47, C2×C41×D141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7708, 11);