Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #546×D61 |
| Fitting | C61×#546 ⋊ C2 |
| Sylow | C61 ⋊ C2×#546 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C61×#546 | C2 |
| hypercenter | #546 | D61 |
| hypocenter | C61 | C2×#546 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #546 | |
1900 conjugacy classes of subgroups.
800 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#3264, D61×#3266, D61×#3267, … |
| maximal normal subgroup of | D61×#3264, D61×#3266, D61×#3267, … |
| maximal quotient of | D4×C22⋊C4×D61, D61×#2339, D61×#2342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17951);