Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11758187 |
| derived, Sylow | C61 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #6923 |
| commutator, hypocenter | C61 | C2×C4×C16 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | C2×C42×C61 | C4 |
| socle | C23×C61 | C2×C8 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C42 | |
216 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | #30594177, #30594188, #30594256, … |
| maximal normal subgroup of | #30594177, #30594188, #30594256, … |
| maximal quotient of | C2×C8×#11758187, C2×#21460732, M16×#11758187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20706);