Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
| direct product | C22×#14519689 |
| Fitting | C23×C8×C61 ⋊ C2 |
| Sylow | C61 ⋊ C22×C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D61 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C23×C8×C61 | C2 |
| socle | C24×C61 | C2×C4 |
| hypercenter | C23×C8 | D61 |
| hypocenter | C61 | C22×C22⋊C8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23×C4 ◁ C23×C8 | |
1072 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 389 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29585229, #29585232, #29585235, … |
| maximal normal subgroup of | #29585229, #29585232, #29585235, … |
| maximal quotient of | C22×#16839485, C22×#16839487, C2×#21444131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 12941);