Finite Group DatabasebetaFinite Group Databasebeta| order | 7708 |
| automorphism | Aut(G) order 7091360 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3854 |
| direct product | C2×D1927 |
| unambiguous semidirect product | (C2×C41)⋊D47 |
| unambiguous semidirect product | (C2×C47)⋊D41 |
| Fitting, socle | C2×C41×C47 ⋊ C2 |
| derived, Hall | C41×C47 ⋊ C22 |
| Sylow | C47 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1927 |
| commutator, hypocenter | C41×C47 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C41×C47 | C2 |
| LCS | G ▷ C41×C47 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1930 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1927, C2×C3×D1927, C2×D5781, … |
| maximal normal subgroup of | C2×C3×D1927, C2×C47⋊(D41⋊C5), C2×C5×D1927, … |
| maximal quotient of | D3×D1927, C2×C3×D1927, C2×D5781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7708, 9);