Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D32×D61 |
| Fitting | C61×D32 ⋊ C2 |
| Sylow | C61 ⋊ C2×D32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D61 |
| commutator | C16×C61 | C23 |
| Frattini | C16 | C22×D61 |
| Fitting | C61×D32 | C2 |
| socle | C2×C61 | C2×D16 |
| hypercenter | D32 | D61 |
| hypocenter | C61 | C2×D32 |
| LCS | G ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32 | |
120 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | D61×D64, D61×SD128, #29601069, … |
| maximal normal subgroup of | D61×D64, D61×SD128, #29601069, … |
| maximal quotient of | D61×#1415, D61×#1423, #29600584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6806);