Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D4×#11758187 |
| Sylow | C61 ⋊ D4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C22×C16 |
| Fitting | C4×D4×C61 | C4 |
| socle | C22×C61 | C22×C8 |
| hypercenter | C4×D4 | #6923 |
| hypocenter | C61 | D4×C16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
174 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 90 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 | D8×#11758187, #30605876, #30605878, … |
| maximal normal subgroup of | D8×#11758187, #30605876, #30605878, … |
| maximal quotient of | D8×#11758187, SD16×#11758187, Q16×#11758187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20887);