Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #443×D61 |
| Fitting | C61×#443 ⋊ C2 |
| Sylow | C61 ⋊ C2×#443 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D61 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#443 | C2 |
| socle | C2×C61 | C2×C4×D4 |
| hypercenter | #443 | D61 |
| hypocenter | C61 | C2×#443 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #443 | |
472 conjugacy classes of subgroups.
896 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1335, #29589798, D61×#1336, … |
| maximal normal subgroup of | D61×#1335, #29589798, D61×#1336, … |
| maximal quotient of | C8×D8×D61, C8×SD16×D61, C8×Q16×D61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13396);