Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #538×D61 |
| Fitting | C61×#538 ⋊ C2 |
| Sylow | C61 ⋊ C2×#538 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C61×#538 | C2 |
| hypercenter | #538 | D61 |
| hypocenter | C61 | C2×#538 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #538 | |
1336 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1600, D61×#1606, D61×#1612, … |
| maximal normal subgroup of | D61×#1600, D61×#1606, D61×#1612, … |
| maximal quotient of | D61×#2312, D61×#2318, D61×#2321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17844);