Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4⋊C4×#92420 |
| Sylow | C61 ⋊ C8×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator | C2×C61 | C2×C4×C8 |
| Fitting | C2×C4⋊C4×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C4⋊C4 | #6923 |
| hypocenter | C61 | C8×C4⋊C4 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
296 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
380 conjugacy classes — view the full character table.
| maximal subgroup of | #102×#92420, #30597669, #103×#92420, … |
| maximal normal subgroup of | #102×#92420, #30597669, #103×#92420, … |
| maximal quotient of | C4⋊C8×#92420, #30597956, #30597970, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20301);