Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C25 |
| direct product | C4×#135×C61 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C61 | D4 |
| commutator | C4 | C23×C4×C61 |
| Frattini, cosocle | C2×C4 | C24×C61 |
| socle | C22×C61 | C22×D4 |
| prime radical | C2×#135×C61 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C61 ◁ C2×C42×C61 ◁ G | |
500 conjugacy classes of subgroups.
3416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 1671);