Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D61⋊M64 |
| Sylow | C61 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | C2×#6923 |
| commutator, socle | C2×C61 | C22×C16 |
| Frattini | C8 | C22×#6923 |
| Fitting | C2×C16×C61 | C4 |
| hypercenter | C2×C16 | #6923 |
| hypocenter | C61 | C2×M64 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C16 ◁ C2×C16 | |
112 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^11,h^c=h^60,h^d=h^60560 conjugacy classes — view the full character table.
| maximal subgroup of | #30595085, #30595088, #30595091, … |
| maximal normal subgroup of | #30595085, #30595088, #30595091, … |
| maximal quotient of | #30608232, #30608237, #30608238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20931);