Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ D4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C22×C16 |
| Fitting | C22⋊C8×C61 | C4 |
| socle | C22×C61 | C22×C8 |
| hypercenter | C22⋊C8 | #6923 |
| hypocenter | C61 | D4×C16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
174 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=e,c^2=e,e^2=f,f^2=g,b^a=bd,h^a=h^50,h^c=h^11,h^e=h^60380 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21462197, D4×D61⋊C16, #30624226, … |
| maximal normal subgroup of | C2×#21462197, D4×D61⋊C16, #30624226, … |
| maximal quotient of | #30605876, #30605912, #30605913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20888);