Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#14519742 |
| Sylow | C61 ⋊ C42×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D61 |
| commutator | C2×C61 | C22×C42 |
| Frattini | C23 | C23×D61 |
| Fitting | C4×C4⋊C4×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C4×C4⋊C4 | D61 |
| hypocenter | C61 | C42×Q8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
684 conjugacy classes of subgroups.
1280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29570609, #29570619, #29570629, … |
| maximal normal subgroup of | #29570609, #29570619, #29570629, … |
| maximal quotient of | C4×#16839613, C4×C4⋊C4×Dic61, #29601185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6859);