Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ Q8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C22×C16 |
| Fitting | C4⋊C8×C61 | C4 |
| socle | C22×C61 | C22×C8 |
| hypercenter | C4⋊C8 | #6923 |
| hypocenter | C61 | Q8×C16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
134 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,b^2=d,c^2=de,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 | #30605912, #30605914, #30605920, … |
| maximal normal subgroup of | #30605912, #30605914, #30605920, … |
| maximal quotient of | #30606695, #30606696, #30607766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20924);