Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D4×#11758217 |
| Sylow | C61 ⋊ D4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C22×D4×C61 | C4 |
| hypercenter | C22×D4 | #6923 |
| hypocenter | C61 | D4×M16 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
544 conjugacy classes of subgroups.
350 conjugacy classes — view the full character table.
| maximal subgroup of | #30600661, #30600665, #30600669, … |
| maximal normal subgroup of | #30600661, #30600665, #30600669, … |
| maximal quotient of | D8×#11758217, #30613415, SD16×#11758217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21246);