Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C61 ⋊ #1313 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×#6923 |
| commutator | C4×C61 | C4×C8 |
| Frattini | C2×C8 | C2×#6923 |
| Fitting | C2×C16×C61 | C4 |
| socle | C22×C61 | #97 |
| hypercenter | C2×C16 | #6923 |
| hypocenter | C61 | #1313 |
| LCS | G ▷ C4×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C16 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^50,c^b=cg,h^b=h^11,h^c=h^60,h^d=h^60524 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460738, #30603704, #30603710, … |
| maximal normal subgroup of | C2×#21460738, #30603704, #30603710, … |
| maximal quotient of | #30594011, #30594178, #30594794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19429);