Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#16840829 |
| unambiguous semidirect product | D61⋊#518 |
| Fitting | C22×D4×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#518 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×#6923 |
| commutator | C2×C61 | C24×C4 |
| Frattini | C2 | C24×#6923 |
| Fitting | C22×D4×C61 | C4 |
| socle | C22×C61 | C23×C4 |
| hypercenter | C22×D4 | #6923 |
| hypocenter | C61 | C2×#518 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
1920 conjugacy classes of subgroups.
368 conjugacy classes — view the full character table.
| maximal subgroup of | #30602436, #30602438, #30602454, … |
| maximal normal subgroup of | #30602436, #30602438, #30602454, … |
| maximal quotient of | C2×#21462255, C2×#21462257, C2×#21462258, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21487);