Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×#11758187 |
| derived, Sylow | C61 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #6923 |
| commutator, hypocenter | C61 | C23×C16 |
| Frattini | C4 | C23×#6923 |
| Fitting | C23×C4×C61 | C4 |
| socle | C24×C61 | C8 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C23×C4 | |
440 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21469);