Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | D4×D61⋊C8 |
| unambiguous semidirect product | D61⋊(C8×D4) |
| Sylow | C61 ⋊ C2×C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C22 | C23×#6923 |
| Fitting | C4×D4×C61 | C4 |
| socle | C22×C61 | C23×C4 |
| hypercenter | C4×D4 | #6923 |
| hypocenter | C61 | C2×C8×D4 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
616 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | #30597670, #30597678, #30597686, … |
| maximal normal subgroup of | #30597670, #30597678, #30597686, … |
| maximal quotient of | D8×D61⋊C8, SD16×D61⋊C8, Q16×D61⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21213);