Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
| direct product | #97×#6923 |
| Fitting | #97×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×#97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C43 |
| Fitting | #97×C61 | C4 |
| socle | C22×C61 | C2×C42 |
| hypercenter | #97 | #6923 |
| hypocenter | C61 | C4×#97 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 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 | #329×#6923, #330×#6923, #30597791, … |
| maximal normal subgroup of | #329×#6923, #330×#6923, #30597791, … |
| maximal quotient of | #322×#6923, #97×#92420, #30595956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20163);