Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14519827 |
| Sylow | C61 ⋊ C22⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×#6923 |
| commutator | C2×C61 | C2×C32 |
| Fitting | C22×C8×C61 | C4 |
| socle | C22×C61 | C2×C16 |
| hypercenter | C22×C8 | #6923 |
| hypocenter | C61 | C22⋊C32 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^11,h^d=h^60560 conjugacy classes — view the full character table.
| maximal subgroup of | #30594796, #30594797, #30594798, … |
| maximal normal subgroup of | #30594796, #30594797, #30594798, … |
| maximal quotient of | #30594796, #30594856, D4⋊#14519827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19623);