Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C241 · Schur multiplier (H2) = C1 |
| direct product | #108×C241 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C241 | D4 |
| commutator | C4 | C2×C4×C241 |
| Frattini, cosocle | C2×C4 | C22×C241 |
| socle | C2×C241 | C4⋊C4 |
| prime radical | C22×C241 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C241 ◁ C2×C4×C241 ◁ G | |
30 conjugacy classes of subgroups.
3374 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 15);