Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16840650 |
| Sylow | C61 ⋊ C2×#346 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6923 |
| commutator | C2×C61 | C2×C4×C8 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | C2×C42×C61 | C4 |
| socle | C23×C61 | C2×C8 |
| hypercenter | C2×C42 | #6923 |
| hypocenter | C61 | C2×#346 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
200 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #30594179, #30594185, #30594264, … |
| maximal normal subgroup of | #30594179, #30594185, #30594264, … |
| maximal quotient of | C2×#21460731, C2×#21460734, #30603731, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20710);