Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×#92420 |
| Sylow | C61 ⋊ C2×C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C22 | C23×#6923 |
| Fitting | C22×Q8×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C22×Q8 | #6923 |
| hypocenter | C61 | C2×C8×Q8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
440 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 274 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 | #101×#92420, #30597530, #103×#92420, … |
| maximal normal subgroup of | #101×#92420, #30597530, #103×#92420, … |
| maximal quotient of | C2×C4⋊C4×#92420, C4×Q8×#92420, C2×#21461872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21291);