Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#92420⋊C8 |
| Sylow | C61 ⋊ C2×#322 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6923 |
| commutator | C2×C61 | C2×C4×C8 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | C22×C8×C61 | C4 |
| socle | C23×C61 | C42 |
| hypercenter | C22×C8 | #6923 |
| hypocenter | C61 | C2×#322 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
248 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #30594362, #30594365, C4×#92420⋊C8, … |
| maximal normal subgroup of | #30594362, #30594365, C4×#92420⋊C8, … |
| maximal quotient of | C4×#92420⋊C8, C2×#21460641, #30597375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19705);