Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#16840605 |
| Sylow | C61 ⋊ C2×#323 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22⋊#6923 |
| commutator | C22×C61 | C22×C8 |
| Frattini | C23 | C22×#6923 |
| Fitting | C25×C61 | C4 |
| socle | C23×C61 | C22⋊C4 |
| hypercenter | C25 | #6923 |
| hypocenter | C61 | C2×#323 |
| LCS | G ▷ C22×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C24 ◁ C25 | |
456 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
524 conjugacy classes — view the full character table.
| maximal subgroup of | #30594339, #30594340, C4×#16840605, … |
| maximal normal subgroup of | #30594339, #30594340, C4×#16840605, … |
| maximal quotient of | C2×#21460635, C2×#21460639, #30595342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19735);