Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16840630 |
| Fitting | C22×C8×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×#6923 |
| commutator | C4×C61 | C2×C42 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | C22×C8×C61 | C4 |
| socle | C22×C61 | #95 |
| hypercenter | C22×C8 | #6923 |
| hypocenter | C61 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C8 | |
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
524 conjugacy classes — view the full character table.
| maximal subgroup of | #30594560, #30594562, #30594568, … |
| maximal normal subgroup of | #30594560, #30594562, #30594568, … |
| maximal quotient of | C2×#21460642, #30596006, #30596011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20181);