Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C22×#14519717 |
| Sylow | C61 ⋊ C22×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D61 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C8 | C23×D61 |
| Fitting | C23×C8×C61 | C2 |
| socle | C23×C61 | C2×C8 |
| hypercenter | C23×C8 | D61 |
| hypocenter | C61 | C22×M32 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C8 ◁ C23×C8 | |
400 conjugacy classes of subgroups.
2000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29594852, #29594853, #29594855, … |
| maximal normal subgroup of | #29594852, #29594853, #29594855, … |
| maximal quotient of | C22×#16839538, C2×C4×#14519717, C22×C22⋊#11758185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17606);