Finite Group DatabasebetaFinite Group Databasebeta| order | 7708 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×#4223 |
| Fitting, socle, Hall | C41×C47 ⋊ C4 |
| derived, Sylow | C41 ⋊ C4×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | #4223 |
| commutator, hypocenter | C41 | C4×C47 |
| Frattini | C1 | G |
| Fitting, socle | C41×C47 | C4 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C47 | |
12 conjugacy classes of subgroups.
658 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C47×#4223, C47×C3⋊#4223, C47×#4223⋊C5, … |
| maximal normal subgroup of | C3×C47×#4223, C47×#4223⋊C5, C5×C47×#4223 |
| maximal quotient of | C3×C47×#4223, C47×C3⋊#4223, C5×C47×#4223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7708, 6);