Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D61⋊C64 |
| derived, Sylow | C61 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #6923 |
| commutator, hypocenter | C61 | C2×C64 |
| Frattini | C16 | C2×#6923 |
| Fitting | C32×C61 | C4 |
| socle | C2×C61 | C2×C32 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C32 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^11,h^b=h^60,h^c=h^60608 conjugacy classes — view the full character table.
| maximal subgroup of | C64×#6923, #30595232, #30595297, … |
| maximal normal subgroup of | C64×#6923, #30595232, #30595297, … |
| maximal quotient of | #30595231, #30595240, #30595306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19678);