Finite Group DatabasebetaFinite Group Databasebeta| order | 7708 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×Dic41 |
| derived, Sylow | C41 ⋊ C4×C47 |
| Hall | C41×C47 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C47 | D41 |
| commutator, hypocenter | C41 | C4×C47 |
| Frattini | C2 | C47×D41 |
| Fitting, socle | C2×C41×C47 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C47 | |
12 conjugacy classes of subgroups.
2068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C47×Dic41, C47×Dic123, C5×C47×Dic41, … |
| maximal normal subgroup of | C3×C47×Dic41, C5×C47×Dic41, C47×Dic41⋊C5 |
| maximal quotient of | C3×C47×Dic41, C47×Dic123, C5×C47×Dic41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7708, 2);