Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | C2×#16840694 |
| Sylow | C61 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×#6923 |
| commutator | C2×C61 | C22×C16 |
| Frattini | C8 | C22×#6923 |
| Fitting | C22×C8×C61 | C4 |
| socle | C22×C61 | C2×C16 |
| hypercenter | C22×C8 | #6923 |
| hypocenter | C61 | C2×M64 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
112 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #30595083, #30595084, #30595086, … |
| maximal normal subgroup of | #30595083, #30595084, #30595086, … |
| maximal quotient of | C2×#21460926, C4×#16840694, C2×C22⋊#14519827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20930);