Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #424×D61 |
| Fitting | C61×#424 ⋊ C2 |
| Sylow | C61 ⋊ C2×#424 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C61×#424 | C2 |
| hypercenter | #424 | D61 |
| hypocenter | C61 | C2×#424 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #424 | |
512 conjugacy classes of subgroups.
896 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1323, #29589155, #29589158, … |
| maximal normal subgroup of | D61×#1323, #29589155, #29589158, … |
| maximal quotient of | D61×#1570, D61×#1571, D61×#1572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13066);