Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C22×#14519852 |
| Sylow | C61 ⋊ C22×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C4 | C23×#6923 |
| Fitting | C22×C8×C61 | C4 |
| socle | C23×C61 | C2×C8 |
| hypercenter | C22×C8 | #6923 |
| hypocenter | C61 | C22×M32 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
400 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #30606139, #30606143, C2×#21460859, … |
| maximal normal subgroup of | #30606139, #30606143, C2×#21460859, … |
| maximal quotient of | C22×#16840651, C2×C4×#14519852, C22×#16840657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21473);