Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#16840820 |
| Sylow | C61 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C4 | C23×#6923 |
| Fitting | C2×#41×C61 | C4 |
| socle | C22×C61 | C22×C8 |
| hypercenter | C2×#41 | #6923 |
| hypocenter | C61 | C2×#504 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
368 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | #30606458, #30606459, #30606463, … |
| maximal normal subgroup of | #30606458, #30606459, #30606463, … |
| maximal quotient of | C2×#21462028, C4×#16840820, C2×#21462049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21474);