Finite Group DatabasebetaFinite Group Databasebeta| order | 7708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D41×D47 |
| unambiguous semidirect product | (C47×D41)⋊C2 |
| unambiguous semidirect product | (C41×D47)⋊C2 |
| unambiguous semidirect product | D1927⋊C2 |
| Fitting, socle, derived, Hall | C41×C47 ⋊ C22 |
| Sylow | C47 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C41×C47 | C22 |
| LCS | G ▷ C41×C47 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
550 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D41×D47, D47×D123, D41×D141, … |
| maximal normal subgroup of | C3×D41×D47, D47×D41⋊C5, C5×D41×D47 |
| maximal quotient of | C3×D41×D47, D47×D123, D41×D141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7708, 8);