Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C26 |
| direct product | D4×D8×C61 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C61 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C4×D4×C61 ◁ G | |
620 conjugacy classes of subgroups.
2135 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2011);