Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C22×#14519771 |
| Fitting | C22×C42×C61 ⋊ C2 |
| Sylow | C61 ⋊ C22×#126 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D61 |
| commutator | C22×C61 | C25 |
| Frattini | C22 | C24×D61 |
| Fitting | C22×C42×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C22×C42 | D61 |
| hypocenter | C61 | C22×#126 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
1320 conjugacy classes of subgroups.
1976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29571375, #29604535, #29604539, … |
| maximal normal subgroup of | #29571375, #29604535, #29604539, … |
| maximal quotient of | C22×#16839630, C22×#16839646, C22×#16839653, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17766);