Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#92420 |
| Sylow | C61 ⋊ C22×C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C22 | C23×#6923 |
| Fitting | C25×C61 | C4 |
| socle | C24×C61 | C2×C4 |
| hypercenter | C25 | #6923 |
| hypocenter | C61 | C22×C22⋊C8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C25 | |
1072 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 378 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
560 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460657, #30596242, #30596259, … |
| maximal normal subgroup of | C2×#21460657, #30596242, #30596259, … |
| maximal quotient of | C22×#16840605, C22×#16840607, C2×#21461050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21083);