Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×D61⋊C32 |
| unambiguous semidirect product | D61⋊(C2×C32) |
| derived, Sylow | C61 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #6923 |
| commutator, hypocenter | C61 | C22×C32 |
| Frattini | C8 | C22×#6923 |
| Fitting | C2×C16×C61 | C4 |
| socle | C22×C61 | C2×C16 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C16 | |
120 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#6923)⋊C32, #30595098, #30595099, … |
| maximal normal subgroup of | (C2×#6923)⋊C32, #30595098, #30595099, … |
| maximal quotient of | C4×D61⋊C32, C2×#21460924, D61⋊(C22⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20929);