Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | #41×#92420 |
| Sylow | C61 ⋊ C8×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C22 | C23×#6923 |
| Fitting | C2×#41×C61 | C4 |
| socle | C22×C61 | C23×C4 |
| hypercenter | C2×#41 | #6923 |
| hypocenter | C61 | C8×#41 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
456 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
380 conjugacy classes — view the full character table.
| maximal subgroup of | #104×#92420, #30597626, #30597632, … |
| maximal normal subgroup of | #104×#92420, #30597626, #30597632, … |
| maximal quotient of | #117×#92420, C4×D4×#92420, C4×Q8×#92420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21313);